subject:(Automatic differentiation)

University of Waterloo

1. Embaye, Samuel. The determination of structured Hessian matrices via automatic differentiation.

Degree: 2014, University of Waterloo

► In using automatic differentiation (AD) for Hessian computation, efficiency can be achieved by exploiting the sparsity existing in the derivative matrix. However, in the case… (more)

Subjects/Keywords: automatic differentiation; structure; gradient; Hessian

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APA (6^th Edition):

Embaye, S. (2014). The determination of structured Hessian matrices via automatic differentiation. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/8850

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Embaye, Samuel. “The determination of structured Hessian matrices via automatic differentiation.” 2014. Thesis, University of Waterloo. Accessed January 17, 2021. http://hdl.handle.net/10012/8850.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Embaye, Samuel. “The determination of structured Hessian matrices via automatic differentiation.” 2014. Web. 17 Jan 2021.

Vancouver:

Embaye S. The determination of structured Hessian matrices via automatic differentiation. [Internet] [Thesis]. University of Waterloo; 2014. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10012/8850.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Embaye S. The determination of structured Hessian matrices via automatic differentiation. [Thesis]. University of Waterloo; 2014. Available from: http://hdl.handle.net/10012/8850

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Manchester

2. Kozikowski, Grzegorz Lukasz. Calibration of financial models based on Automatic Differentiation and High-Performance Computing.

Degree: 2018, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:314098

► Stochastic models are commonly used in quantitative finance to describe the dynamics of the derivatives market. As the market quotes are constantly changing, the models… (more)

▼ Stochastic models are commonly used in quantitative finance to describe the dynamics of the derivatives market. As the market quotes are constantly changing, the models need to be calibrated to make real-time investment decisions. This can involve the sensitivity calculation to support the calibration process and investment portfolio management. For investment portfolios consisting of thousands of assets and options, the sensitivity calculation and calibration process are computationally expensive. This thesis presents a number of approaches to sensitivity calculation and model calibration utilizing high-performance computing architectures and Automatic Differentiation that improve performance and accuracy in financial modeling when compared to finite differences and pathwise methods. A parallel Monte-Carlo engine has been developed using the Adjoint methods for the first-order sensitivity calculation and model calibration This addresses the sensitivity and calibration problem for general stochastic differential models. The engine supports multi-/many-core CPU, GPU and distributed computing architectures. The work utilizes a graph representation and overloading operators to express general stochastic differential models. The sensitivities for the model calibration are calculated in parallel via a single simulation by the Adjoint method with the gradient computation cost being 1.8x that of function evaluation. The computational experiments consider both the Heston model and Heston with term-structure. These show that the engine improves performance by up to two orders of magnitude when compared to a sequential version. A hardware implementation has been developed for the Heston model calibration via the Adjoint on FPGA. The work also shows performance improvement of up to two orders of magnitude when compared to a sequential implementation. A parallel non-linear least squares optimization framework using Automatic Differentiation has been developed. This utilizes a graph representation and overloaded operator techniques to express the general objective and constraint functions. The framework supports multi-/many-core architectures such as GPUs and Intel Xeon/Xeon-Phi. The computational experiments consider the semi-closed form Heston model with the Gauss-Kronrod integration. These show performance improvement of 8.4x on GPU (OpenCL) and 7x on (CUDA) vs a sequential OMP (OpenMP) implementation. A Xeon-Phi implementation improves performance by 34x when compared to a single-thread implementation. Advisors/Committee Members: ZENG, XIAOJUN X, Keane, John, Zeng, Xiaojun.

Subjects/Keywords: calibration; Automatic Differentiation; HPC

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APA (6^th Edition):

Kozikowski, G. L. (2018). Calibration of financial models based on Automatic Differentiation and High-Performance Computing. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:314098

Chicago Manual of Style (16^th Edition):

Kozikowski, Grzegorz Lukasz. “Calibration of financial models based on Automatic Differentiation and High-Performance Computing.” 2018. Doctoral Dissertation, University of Manchester. Accessed January 17, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:314098.

MLA Handbook (7^th Edition):

Kozikowski, Grzegorz Lukasz. “Calibration of financial models based on Automatic Differentiation and High-Performance Computing.” 2018. Web. 17 Jan 2021.

Vancouver:

Kozikowski GL. Calibration of financial models based on Automatic Differentiation and High-Performance Computing. [Internet] [Doctoral dissertation]. University of Manchester; 2018. [cited 2021 Jan 17]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:314098.

Council of Science Editors:

Kozikowski GL. Calibration of financial models based on Automatic Differentiation and High-Performance Computing. [Doctoral Dissertation]. University of Manchester; 2018. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:314098

University of Toronto

3. Paige, Cody. Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver.

Degree: 2013, University of Toronto

URL: http://hdl.handle.net/1807/35661

►

The use of adjoint methods is common in computational fluid dynamics to reduce the cost of the sensitivity analysis in an optimization cycle. The forward… (more)

Subjects/Keywords: Laminar Navier-Stokes; adjoint; automatic differentiation; 0538

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Paige, C. (2013). Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/35661

Chicago Manual of Style (16^th Edition):

Paige, Cody. “Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver.” 2013. Masters Thesis, University of Toronto. Accessed January 17, 2021. http://hdl.handle.net/1807/35661.

MLA Handbook (7^th Edition):

Paige, Cody. “Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver.” 2013. Web. 17 Jan 2021.

Vancouver:

Paige C. Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver. [Internet] [Masters thesis]. University of Toronto; 2013. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/1807/35661.

Council of Science Editors:

Paige C. Extension of the ADjoint Approach to a Laminar Navier-Stokes Solver. [Masters Thesis]. University of Toronto; 2013. Available from: http://hdl.handle.net/1807/35661

Georgia Tech

4. Yonge, Adam Christopher. Generalized Simulation and Processing of TAP Reactor Data.

Degree: MS, Chemical and Biomolecular Engineering, 2020, Georgia Tech

URL: http://hdl.handle.net/1853/63499

► An understanding of intrinsic kinetics is necessary for the rational design of new materials for catalytic processes. One way to obtain this information is by… (more)

▼ An understanding of intrinsic kinetics is necessary for the rational design of new materials for catalytic processes. One way to obtain this information is by running and interpreting Temporal Analysis of Products (TAP) reactor experiments. Though these experiments provide rich, transient kinetic information, converting the raw TAP data to knowledge of the material is a major bottleneck. Steps have previously been taken to reduce this burden, but further developments, as well as refinement of current methods, are needed. One change that could improve processing is the application of automatic differentiation (AD), which offers a highly accurate calculation of the derivative. For this reason, a workflow to simulate and process TAP reactor pulses built around the FEniCS Python package has been developed. This package allows for the efficient evaluation of the necessary PDEs for TAP, and allows for efficient AD by taking advantage of the adjoint operators of the PDE. A method to convert elementary reactions directly into the FEniCS PDE format was developed. The first steps to generate reaction mechanisms, as well as sets of rate-limiting reaction expressions, based on the gaseous reactants and products observed during TAP experiments were also taken. The new, general method of simulating pulses around FEniCS was validated and benchmarked. The time required for each simulation was not found to limit the workflows ability to quickly handle TAP data, but improvements can be made. The Degree of Flux Control was also introduced as an alternate form to the commonly used Degree of Rate Control. This is the first example of a transient sensitivity analysis performed on TAP pulses, and one of few implementations of the Degree of Rate Control analysis to transient processes. A method to fit parameters was also implemented, and objective functions were constructed with a reduced number of points to improve efficiency. The parameter fitting method was applied to several examples, including pure diffusion, a linear reaction mechanism, and multiple carbon monoxide oxidation reaction mechanisms, and was found to accurately determine diffusive and kinetic parameters. The methods developed in this Thesis show the utility of AD and should lead to a more efficient processing of TAP data. This workflow will act as a foundation on which more advanced methods can be developed, including forward and reverse uncertainty quantification, the generation of initial parameter estimates for fitting, and the application to increasingly complex reaction networks. Ultimately, it is envisioned that these methods can work in concert with experiments, providing a route to adaptive TAP experiments that automatically interrogate the intrinsic kinetics of real catalytic materials. Advisors/Committee Members: Medford, Andrew J (advisor), Sievers, Carsten (advisor), Isaac, Tobin (advisor).

Subjects/Keywords: Temporal Analysis of Products; Automatic Differentiation

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APA (6^th Edition):

Yonge, A. C. (2020). Generalized Simulation and Processing of TAP Reactor Data. (Masters Thesis). Georgia Tech. Retrieved from http://hdl.handle.net/1853/63499

Chicago Manual of Style (16^th Edition):

Yonge, Adam Christopher. “Generalized Simulation and Processing of TAP Reactor Data.” 2020. Masters Thesis, Georgia Tech. Accessed January 17, 2021. http://hdl.handle.net/1853/63499.

MLA Handbook (7^th Edition):

Yonge, Adam Christopher. “Generalized Simulation and Processing of TAP Reactor Data.” 2020. Web. 17 Jan 2021.

Vancouver:

Yonge AC. Generalized Simulation and Processing of TAP Reactor Data. [Internet] [Masters thesis]. Georgia Tech; 2020. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/1853/63499.

Council of Science Editors:

Yonge AC. Generalized Simulation and Processing of TAP Reactor Data. [Masters Thesis]. Georgia Tech; 2020. Available from: http://hdl.handle.net/1853/63499

University of Arizona

5. Chernikov, Dmitry. PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance .

Degree: 2017, University of Arizona

URL: http://hdl.handle.net/10150/626368

► In this dissertation we investigate methods of solving various optimization problems with PDE constraints, i.e. optimization problems that have a system of partial differential equations… (more)

Subjects/Keywords: adjoint differentiation; automatic differentiation; multiphysics; nonlinear optimization; optimization of portfolio of options; PDE-constrained optimization

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chernikov, D. (2017). PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/626368

Chicago Manual of Style (16^th Edition):

Chernikov, Dmitry. “PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance .” 2017. Doctoral Dissertation, University of Arizona. Accessed January 17, 2021. http://hdl.handle.net/10150/626368.

MLA Handbook (7^th Edition):

Chernikov, Dmitry. “PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance .” 2017. Web. 17 Jan 2021.

Vancouver:

Chernikov D. PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance . [Internet] [Doctoral dissertation]. University of Arizona; 2017. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10150/626368.

Council of Science Editors:

Chernikov D. PDE Constrained Optimization in Stochastic and Deterministic Problems of Multiphysics and Finance . [Doctoral Dissertation]. University of Arizona; 2017. Available from: http://hdl.handle.net/10150/626368

University of Waterloo

6. Koppel, Leonid. On the Manifold: Representing Geometry in C++ for State Estimation.

Degree: 2018, University of Waterloo

URL: http://hdl.handle.net/10012/14264

► Manipulating geometric objects is central to state estimation problems in robotics. Typical algorithms must optimize over non-Euclidean states, such as rigid transformations on the SE(3)… (more)

▼ Manipulating geometric objects is central to state estimation problems in robotics. Typical algorithms must optimize over non-Euclidean states, such as rigid transformations on the SE(3) manifold, and handle measurements expressed in multiple coordinate frames. Researchers typically rely on C++ libraries for geometric tasks. Commonly used libraries range from linear algebra software such as Eigen to robotics-targeted optimization frameworks such as GTSAM, which provides manifold operations and automatic differentiation of arbitrary expressions. This thesis examines how geometric operations in existing software can be improved, both in runtime performance and in the expression of geometric semantics, to support rapid and error-free development of robotics algorithms. This thesis presents wave_geometry, a C++ manifold geometry library providing representations of objects in affine, Euclidean, and projective spaces, and the Lie groups SO(3) and SE(3). It encompasses the main contributions of this work: an expression template-based automatic differentiation system and compile-time checking of coordinate frame semantics. The library can evaluate Jacobians of geometric expressions in forward and reverse mode with little runtime overhead compared to hand-coded derivatives, and exceeds the performance of existing libraries. While high performance is achieved by taking advantage of compile-time knowledge, the library also provides dynamic expressions which can be composed at runtime. Coordinate frame conversions are a common source of mistakes in calculations. However, the validity of operations can automatically be checked by tracking the coordinate frames associated with each object. A system of rules for propagating coordinate frame semantics though geometric operations, including manifold operations, is developed. A template-based method for checking coordinate frame semantics at compile time, with no runtime overhead, is presented. Finally, this thesis demonstrates an application to state estimation, presenting a framework for formulating nonlinear least squares optimization problems as factor graphs. The framework combines wave_geometry expressions with the widely used Ceres Solver software, and shows the utility of automatically differentiated geometric expressions.

Subjects/Keywords: robotics; computer vision; manifold geometry; software tools; automatic differentiation; coordinate frames

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Koppel, L. (2018). On the Manifold: Representing Geometry in C++ for State Estimation. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/14264

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Koppel, Leonid. “On the Manifold: Representing Geometry in C++ for State Estimation.” 2018. Thesis, University of Waterloo. Accessed January 17, 2021. http://hdl.handle.net/10012/14264.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Koppel, Leonid. “On the Manifold: Representing Geometry in C++ for State Estimation.” 2018. Web. 17 Jan 2021.

Vancouver:

Koppel L. On the Manifold: Representing Geometry in C++ for State Estimation. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10012/14264.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Koppel L. On the Manifold: Representing Geometry in C++ for State Estimation. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/14264

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Virginia Tech

7. Alexe, Mihai. Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems.

Degree: PhD, Computer Science, 2011, Virginia Tech

URL: http://hdl.handle.net/10919/37515

► Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes… (more)

▼ Adaptivity in both space and time has become the norm for solving problems modeled by partial differential equations. The size of the discretized problem makes uniformly refined grids computationally prohibitive. Adaptive refinement of meshes and time steps allows to capture the phenomena of interest while keeping the cost of a simulation tractable on the current hardware. Many fields in science and engineering require the solution of inverse problems where parameters for a given model are estimated based on available measurement information. In contrast to forward (regular) simulations, inverse problems have not extensively benefited from the adaptive solver technology. Previous research in inverse problems has focused mainly on the continuous approach to calculate sensitivities, and has typically employed fixed time and space meshes in the solution process. Inverse problem solvers that make exclusive use of uniform or static meshes avoid complications such as the differentiation of mesh motion equations, or inconsistencies in the sensitivity equations between subdomains with different refinement levels. However, this comes at the cost of low computational efficiency. More efficient computations are possible through judicious use of adaptive mesh refinement, adaptive time steps, and the discrete adjoint method. This dissertation develops a complete framework for fully discrete adjoint sensitivity analysis and inverse problem solutions, in the context of time dependent, adaptive mesh, and adaptive step models. The discrete framework addresses all the necessary ingredients of a stateâ ofâ theâ art adaptive inverse solution algorithm: adaptive mesh and time step refinement, solution grid transfer operators, a priori and a posteriori error analysis and estimation, and discrete adjoints for sensitivity analysis of fluxâ limited numerical algorithms. Advisors/Committee Members: Sandu, Adrian (committeechair), Ribbens, Calvin J. (committee member), Cao, Yang (committee member), De Sturler, Eric (committee member), Borggaard, Jeffrey T. (committee member).

Subjects/Keywords: Inverse problems; Adjoint Method; Adaptive Mesh Refinement; Automatic Differentiation

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APA (6^th Edition):

Alexe, M. (2011). Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/37515

Chicago Manual of Style (16^th Edition):

Alexe, Mihai. “Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems.” 2011. Doctoral Dissertation, Virginia Tech. Accessed January 17, 2021. http://hdl.handle.net/10919/37515.

MLA Handbook (7^th Edition):

Alexe, Mihai. “Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems.” 2011. Web. 17 Jan 2021.

Vancouver:

Alexe M. Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems. [Internet] [Doctoral dissertation]. Virginia Tech; 2011. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10919/37515.

Council of Science Editors:

Alexe M. Adjoint-based space-time adaptive solution algorithms for sensitivity analysis and inverse problems. [Doctoral Dissertation]. Virginia Tech; 2011. Available from: http://hdl.handle.net/10919/37515

Utah State University

8. Hodson, Joshua D. Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio.

Degree: PhD, Mechanical and Aerospace Engineering, 2019, Utah State University

URL: https://digitalcommons.usu.edu/etd/7574

► This work focuses on the development of efficient methods for wing shape optimization for morphing wing technologies. Existing wing shape optimization processes typically rely… (more)

Subjects/Keywords: aerodynamics; optimization; automatic differentiation; lifting line theory; aspect ratio

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APA (6^th Edition):

Hodson, J. D. (2019). Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio. (Doctoral Dissertation). Utah State University. Retrieved from https://digitalcommons.usu.edu/etd/7574

Chicago Manual of Style (16^th Edition):

Hodson, Joshua D. “Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio.” 2019. Doctoral Dissertation, Utah State University. Accessed January 17, 2021. https://digitalcommons.usu.edu/etd/7574.

MLA Handbook (7^th Edition):

Hodson, Joshua D. “Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio.” 2019. Web. 17 Jan 2021.

Vancouver:

Hodson JD. Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio. [Internet] [Doctoral dissertation]. Utah State University; 2019. [cited 2021 Jan 17]. Available from: https://digitalcommons.usu.edu/etd/7574.

Council of Science Editors:

Hodson JD. Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio. [Doctoral Dissertation]. Utah State University; 2019. Available from: https://digitalcommons.usu.edu/etd/7574

9. Sällberg, Gustav. Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions.

Degree: Faculty of Science & Engineering, 2015, Linköping UniversityLinköping University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090

► The master thesis is focused on how a local volatility surfaces can be extracted by optimization with respectto smoothness and price error. The pricing… (more)

Subjects/Keywords: local volatility surface; LVS; optimization; roughness; smooth; risk neutral pricing; optimal growth; pricing error; automatic differentiation; algorithmic differentiation

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APA (6^th Edition):

Sällberg, G. (2015). Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions. (Thesis). Linköping UniversityLinköping University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Sällberg, Gustav. “Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions.” 2015. Thesis, Linköping UniversityLinköping University. Accessed January 17, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Sällberg, Gustav. “Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions.” 2015. Web. 17 Jan 2021.

Vancouver:

Sällberg G. Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions. [Internet] [Thesis]. Linköping UniversityLinköping University; 2015. [cited 2021 Jan 17]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Sällberg G. Thesis - Optimizing Smooth Local Volatility Surfaces with Power Utility Functions. [Thesis]. Linköping UniversityLinköping University; 2015. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120090

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Illinois – Urbana-Champaign

10. Ghosh, Alexander. Multi-CubeSat mission planning enabled through parallel computing.

Degree: PhD, 4048, 2013, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/45554

► Small CubeSat-class satellites are opening up new avenues for science and technology development within the space industry. What was once a purely educational tool has… (more)

▼ Small CubeSat-class satellites are opening up new avenues for science and technology development within the space industry. What was once a purely educational tool has quickly become the newest international exploration platform for low earth orbit missions. These sub-10 kg satellites ride into space as tertiary payloads, kicked out of their launch vehicles after all other satellites have reached their target orbit, and are left to survive in whatever ride-share provided orbit they are deposited into. Due to their small mass and volume, it has been infeasible until very recently to put any form of on-board propulsion on these spacecraft without a significant sacrifice of the science objectives. Current research at the University of Illinois and other institutions will soon lead to the flight of CubeSat-class low thrust, low-power, yet low-specific impulse propellant systems. This technology should enable CubeSats to acquire new orbits from their launch positions, to rendezvous and dock together, or to reconfigure their constellations within orbit. Because of the atypical combination of low-thrust with high propellant mass consumption, a new toolset is needed to assist with planning of both single and cooperative multi-satellite missions. This work contributes a new framework for the calculation of high-fidelity trajectories in low Earth orbit. A shooting method is reformulated as a non-linear programming problem, and wrapped by a novel mesh refinement algorithm, which updates the time discretization based on a cumulative thrust density function. The states are propagated using a higher order explicit Dormand-Prince integrator with an error-adaptive step size. The necessary derivatives and Jacobian are developed in real time using algorithmic differentiation, which allows for significantly higher accuracy over traditional finite difference methods. This framework is tested against analytical methods developed by Wiesel for in-plane, and Edelbaum and Kechichian for out of plane, and is shown to match or surpass their results. This work further contributes to the field by developing an extended framework that allows the simultaneous integration of multiple satellites using parallel processing on a super computer, and lays out the necessary constraints to define cooperative intercept, rendezvous and orbit reconfiguration problems. Finally, this dissertation develops a new approach to parallel algorithmic differentiation, allowing the concurrent calculation of multiple derivatives in a user-transparent manner, simultaneously while propagating multiple satellites. This is accomplished by using a Cartesian processor grid and a new parallel communication scheme to maintain the most data locality per processor, enabling orders of magnitude speedup by comparison to both serial, and the previously developed parallel processing approach. This new parallel algorithmic differentiation technique is demonstrated with a series of test cases, developing cooperative maneuvers for from two to four satellites experiencing… Advisors/Committee Members: Coverstone, Victoria L. (advisor), Coverstone, Victoria L. (Committee Chair), Conway, Bruce A. (committee member), Burton, Rodney L. (committee member), Swenson, Gary R. (committee member).

Subjects/Keywords: satellite; trajectory; trajectory optimization; optimization; cubesat; picosatellite; earth orbit; Orbit; low thrust; low-thrust; automatic differentiation; algorithmic differentiation; parallel processing

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APA (6^th Edition):

Ghosh, A. (2013). Multi-CubeSat mission planning enabled through parallel computing. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/45554

Chicago Manual of Style (16^th Edition):

Ghosh, Alexander. “Multi-CubeSat mission planning enabled through parallel computing.” 2013. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed January 17, 2021. http://hdl.handle.net/2142/45554.

MLA Handbook (7^th Edition):

Ghosh, Alexander. “Multi-CubeSat mission planning enabled through parallel computing.” 2013. Web. 17 Jan 2021.

Vancouver:

Ghosh A. Multi-CubeSat mission planning enabled through parallel computing. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2013. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/2142/45554.

Council of Science Editors:

Ghosh A. Multi-CubeSat mission planning enabled through parallel computing. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2013. Available from: http://hdl.handle.net/2142/45554

University of Oxford

11. Birkisson, Asgeir. Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework.

Degree: PhD, 2013, University of Oxford

URL: http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533

► Ordinary differential equations (ODEs) play an important role in mathematics. Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are… (more)

Subjects/Keywords: 515; Mathematics; Numerical analysis; Ordinary differential equations; nonlinear boundary value problems; automatic differentiation; Frechet derivatives; Chebfun; automatic linearity detection; deflation

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APA (6^th Edition):

Birkisson, A. (2013). Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework. (Doctoral Dissertation). University of Oxford. Retrieved from http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533

Chicago Manual of Style (16^th Edition):

Birkisson, Asgeir. “Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework.” 2013. Doctoral Dissertation, University of Oxford. Accessed January 17, 2021. http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533.

MLA Handbook (7^th Edition):

Birkisson, Asgeir. “Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework.” 2013. Web. 17 Jan 2021.

Vancouver:

Birkisson A. Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework. [Internet] [Doctoral dissertation]. University of Oxford; 2013. [cited 2021 Jan 17]. Available from: http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533.

Council of Science Editors:

Birkisson A. Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework. [Doctoral Dissertation]. University of Oxford; 2013. Available from: http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.647533

University of Illinois – Chicago

12. Yoffe, Genady. Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving.

Degree: 2012, University of Illinois – Chicago

URL: http://hdl.handle.net/10027/9116

► Solving polynomial systems by homotopy continuation consists of two stages: we first define a family of systems, the homotopy, and then we track the solution… (more)

▼ Solving polynomial systems by homotopy continuation consists of two stages: we first define a family of systems, the homotopy, and then we track the solution paths defined by the homotopy. Tracking all paths is a pleasingly parallel computation. The problem we consider in this thesis is tracking one solution path when use of extended precision is required. While tracking only one solution path could occur for systems of larger dimensions and degrees, as it is no longer feasible to compute all solutions, the need to track one difficult path with multiprecision arithmetic often arises for bigger systems. The main subject of this thesis is compensating for the extra cost of double double (DD) and of quad double (QD) precision in path tracking for sparse polynomial systems of moderate sizes by employing multiple cores. First we obtained a scalable multithreaded DD/QD version of Newton's method and subsequently of a path tracker. We achieved on eight cores for moderate systems close to maximal speedups in quad double path tracking. It appeared that in dimensions in which our DD/QD multithreaded path tracker achieves good speedups, with the use of some widely accepted algorithms for sparse polynomial systems, which we originally integrated into our multithreaded path tracker and its input processing procedure, both the path tracking and input processing take an unacceptably long time. Subsequently we have greatly increased the efficiency of our multithreaded implementation in working dimensions by improvements in three different directions. First we suggested a new input processing procedure based on functionality of a Standard Template Library (STL) sorted associative container. Secondly we came up with a choice of much more suitable predictor. Thirdly we integrated into our multithreaded implementation a prudent algorithm for polynomial evaluation and diﬀerentiation, which is based on the ideas of reverse mode Automatic Diﬀerentiation (AD). Recently we eﬃciently accelerated with general purpose graphics unit the same AD-like algorithm for polynomial evaluation and diﬀerentiation. We obtained two digit speedups for moderate systems as hardware double arithmetic is used. Advisors/Committee Members: Verschelde, Jan (advisor), Friedland, Shmuel (committee member), Leykin, Anton (committee member), Nicholls, David (committee member), Turan, Gyorgy (committee member).

Subjects/Keywords: Multithreaded; Graphics Processing Unit; Compute Uniﬁed Device Architecture; Automatic Differentiation; GPU; CUDA; AD

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yoffe, G. (2012). Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/9116

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yoffe, Genady. “Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving.” 2012. Thesis, University of Illinois – Chicago. Accessed January 17, 2021. http://hdl.handle.net/10027/9116.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yoffe, Genady. “Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving.” 2012. Web. 17 Jan 2021.

Vancouver:

Yoffe G. Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving. [Internet] [Thesis]. University of Illinois – Chicago; 2012. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10027/9116.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yoffe G. Using Parallelism to Compensate for Extended Precision in Path Tracking for Polynomial System Solving. [Thesis]. University of Illinois – Chicago; 2012. Available from: http://hdl.handle.net/10027/9116

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Linköping University

13. Hjelmberg, David. Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation.

Degree: Production Economics, 2014, Linköping University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875

► In this master thesis we have examined the possibility of pricing multiple American options, on an underlying asset with discrete dividends, with a finite… (more)

Subjects/Keywords: American options; BSM PDE; discrete dividends; forward PDE; local volatility surface; automatic differentiation

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APA (6^th Edition):

Hjelmberg, D. (2014). Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation. (Thesis). Linköping University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Hjelmberg, David. “Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation.” 2014. Thesis, Linköping University. Accessed January 17, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Hjelmberg, David. “Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation.” 2014. Web. 17 Jan 2021.

Vancouver:

Hjelmberg D. Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation. [Internet] [Thesis]. Linköping University; 2014. [cited 2021 Jan 17]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Hjelmberg D. Pricing of American options with discrete dividends using a PDE and a volatility surface while calculating derivatives with automatic differentiation. [Thesis]. Linköping University; 2014. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-110875

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Ohio University

14. Heller, Richard. Checkpointing without operating system intervention: Implementing Griewank's algorithm.

Degree: MS, Electrical Engineering & Computer Science (Engineering and Technology), 1998, Ohio University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831

Checkpointing without operating system intervention: Implementing Griewank's algorithm Advisors/Committee Members: Juedes, David (Advisor).

Subjects/Keywords: Griewank's Algorithm; Automatic Differentiation; LogAD Compiler

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Heller, R. (1998). Checkpointing without operating system intervention: Implementing Griewank's algorithm. (Masters Thesis). Ohio University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831

Chicago Manual of Style (16^th Edition):

Heller, Richard. “Checkpointing without operating system intervention: Implementing Griewank's algorithm.” 1998. Masters Thesis, Ohio University. Accessed January 17, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831.

MLA Handbook (7^th Edition):

Heller, Richard. “Checkpointing without operating system intervention: Implementing Griewank's algorithm.” 1998. Web. 17 Jan 2021.

Vancouver:

Heller R. Checkpointing without operating system intervention: Implementing Griewank's algorithm. [Internet] [Masters thesis]. Ohio University; 1998. [cited 2021 Jan 17]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831.

Council of Science Editors:

Heller R. Checkpointing without operating system intervention: Implementing Griewank's algorithm. [Masters Thesis]. Ohio University; 1998. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1176494831

Ohio University

15. Kang, Yixiu. Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications.

Degree: MS, Electrical Engineering & Computer Science (Engineering and Technology), 2003, Ohio University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867

► In this work, we present two C/C++ implementations of general purpose automatic differentiation (AD) for GNU Octave applications: FAD for forward mode AD and… (more)

Subjects/Keywords: Computer Science; Automatic Differentiation (AD); Forward Mode Automatic Differentiation; Reverse Mode Automatic Differentiation; Checkpointing; Scientific Computing; Computational Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kang, Y. (2003). Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications. (Masters Thesis). Ohio University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867

Chicago Manual of Style (16^th Edition):

Kang, Yixiu. “Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications.” 2003. Masters Thesis, Ohio University. Accessed January 17, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867.

MLA Handbook (7^th Edition):

Kang, Yixiu. “Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications.” 2003. Web. 17 Jan 2021.

Vancouver:

Kang Y. Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications. [Internet] [Masters thesis]. Ohio University; 2003. [cited 2021 Jan 17]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867.

Council of Science Editors:

Kang Y. Implementation of Forward and Reverse Mode Automatic Differentiation for GNU Octave Applications. [Masters Thesis]. Ohio University; 2003. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1049467867

Universidade do Rio Grande do Sul

16. Espath, Luis Felipe da Rosa. Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos.

Degree: 2013, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/85033

►

Neste trabalho buscou-se consolidar aspectos referentes à otimização de problemas envolvidos na mecânica dos meios contínuos, envolvendo diferentes áreas do conhecimento, tais como: otimização matemática,… (more)

▼

Neste trabalho buscou-se consolidar aspectos referentes à otimização de problemas envolvidos na mecânica dos meios contínuos, envolvendo diferentes áreas do conhecimento, tais como: otimização matemática, diferenciação automática, análise estrutural, análise aerodinâmica, parametrização de curvas, superfícies e sólidos do tipo B-spline racionais não-uniformes (NURBS, acrônimo do inglês), análise IsoGeométrica (IGA, acrônimo do inglês) e análise por Elementos Finitos (FEA, acrônimo do inglês). Como objetivo final busca-se otimizar formas de cascas estruturais e formas de corpos aerodinâmicos imersos em escoamentos compressíveis. No que concerne à análise estrutural, esta é realizada via análise IsoGeométrica utilizando elementos sólidos para modelar cascas. Uma cinemática co-rotacional abrangente e precisa baseada na exata decomposição polar é desenvolvida, para lidar com problemas estáticos e dinâmicos altamente não lineares. Na análise estática foram implementados o método de Newton-Raphson e controle de deslocamentos generalizado, para problemas dinâmicos foram implementados o método -generalizado (G ) e o método energia momento generalizado (GEMM+ ). A análise aerodinâmica é realizada via análise por Elementos Finitos para modelar escoamentos compressíveis viscosos e não viscosos em regimes transônicos e supersônicos. Um esquema característico baseado na separação da equação de momento (CBS, acrônimo do inglês) é utilizado para obter uma adequada integração temporal. No que concerne à otimização matemática, é utilizado um método baseado em gradientes, conhecido por programação quadrática sequencial (SQP, acrônimo do inglês), onde a avaliação as derivadas de Fréchet são levadas a cabo via diferenciação automática (AD, acrônimo do inglês). No que concerne aos resultados finais é realizada a otimização estrutural de forma de cascas modeladas como sólidos são apresentados, evidenciando um desempenho ótimo com respeito à energia de deformação interna. Os resultados de otimização aerodinâmica bidimensionais apresentam perfis aerodinâmicos ótimos com respeito à relação arrasto/sustentação para uma ampla gama de número de Mach, enquanto um resultado tridimensional é apresentado evidenciando a robustez e eficiência da implementação proposta. Pretendese estabelecer com este trabalho as bases para pesquisas em problemas de otimização aeroelástica.

Consolidation of the link among optimization problems in continuum mechanics, involving different fields, such as mathematical optimization, automatic differentiation, structural analysis, aerodynamic analysis, curves, surfaces and solids parameterization using Non Uniform Rational B-spline (NURBS), IsoGeometric Analysis (IGA), Finite Element Analysis (FEA) is looked for. Structural shape optimization of shell structures and aerodynamic shape optimization of immersed bodies in compressible flows are the main goals of this work. Concerning structural analysis, the so-called IsoGeometric analysis is employed. An accurate and comprehensive corotational kinematic based on the…

Advisors/Committee Members: Awruch, Armando Miguel.

Subjects/Keywords: Mathematical optimization; Estruturas (Engenharia); Structural IsoGeometric analysis; Mecânica do contínuo; Otimização matemática; Aerodynamic finite element analysis; Elementos finitos; NURBS; Automatic differentiation

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Espath, L. F. d. R. (2013). Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/85033

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Espath, Luis Felipe da Rosa. “Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos.” 2013. Thesis, Universidade do Rio Grande do Sul. Accessed January 17, 2021. http://hdl.handle.net/10183/85033.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Espath, Luis Felipe da Rosa. “Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos.” 2013. Web. 17 Jan 2021.

Vancouver:

Espath LFdR. Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2013. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10183/85033.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Espath LFdR. Otimização de forma estrutural e aerodinâmica usando análise IsoGeométrica e Elementos Finitos. [Thesis]. Universidade do Rio Grande do Sul; 2013. Available from: http://hdl.handle.net/10183/85033

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Colorado

17. Dunham, Benjamin Zane. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.

Degree: PhD, 2017, University of Colorado

URL: https://scholar.colorado.edu/asen_gradetds/228

► This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common… (more)

▼ This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions – most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series – without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed “stencils,” each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the “forward mode” is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N – i.e., O(1) – the N × N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive – e.g., a N × N × N rank-three tensor can be found in O(N²). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics. Advisors/Committee Members: Kurt K. Maute, Ryan P. Starkey, Alireza Doostan.

Subjects/Keywords: adjoint; automatic differentiation; complex step; hessian-vector; linear algebra; nilpotent element; Aerospace Engineering; Applied Mathematics; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dunham, B. Z. (2017). High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/228

Chicago Manual of Style (16^th Edition):

Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 17, 2021. https://scholar.colorado.edu/asen_gradetds/228.

MLA Handbook (7^th Edition):

Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Web. 17 Jan 2021.

Vancouver:

Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 17]. Available from: https://scholar.colorado.edu/asen_gradetds/228.

Council of Science Editors:

Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/asen_gradetds/228

University of Colorado

18. Dunham, Benjamin Zane. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.

Degree: PhD, 2017, University of Colorado

URL: https://scholar.colorado.edu/asen_gradetds/167

► This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common… (more)

▼ This work presents a new automatic differentiation method, Nilpotent Matrix Differentiation (NMD), capable of propagating any order of mixed or univariate derivative through common linear algebra functions – most notably third-party sparse solvers and decomposition routines, in addition to basic matrix arithmetic operations and power series – without changing data-type or modifying code line by line; this allows differentiation across sequences of arbitrarily many such functions with minimal implementation effort. NMD works by enlarging the matrices and vectors passed to the routines, replacing each original scalar with a matrix block augmented by derivative data; these blocks are constructed with special sparsity structures, termed “stencils,” each designed to be isomorphic to a particular multidimensional hypercomplex algebra. The algebras are in turn designed such that Taylor expansions of hypercomplex function evaluations are finite in length and thus exactly track derivatives without approximation error. Although this use of the method in the “forward mode” is unique in its own right, it is also possible to apply it to existing implementations of the (first-order) discrete adjoint method to find high-order derivatives with lowered cost complexity; for example, for a problem with N inputs and an adjoint solver whose cost is independent of N – i.e., O(1) – the N × N Hessian can be found in O(N) time, which is comparable to existing second-order adjoint methods that require far more problem-specific implementation effort. Higher derivatives are likewise less expensive – e.g., a N × N × N rank-three tensor can be found in O(N²). Alternatively, a Hessian-vector product can be found in O(1) time, which may open up many matrix-based simulations to a range of existing optimization or surrogate modeling approaches. As a final corollary in parallel to the NMD-adjoint hybrid method, the existing complex-step differentiation (CD) technique is also shown to be capable of finding the Hessian-vector product. All variants are implemented on a stochastic diffusion problem and compared in-depth with various cost and accuracy metrics. Advisors/Committee Members: Kurt K. Maute, Ryan P. Starkey, Alireza Doostan, Brian M. Argrow, Bengt Fornberg.

Subjects/Keywords: adjoint; automatic differentiation; complex step; Hessian-vector; linear algebra; nilpotent element; Aerospace Engineering; Applied Mathematics; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dunham, B. Z. (2017). High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/asen_gradetds/167

Chicago Manual of Style (16^th Edition):

Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Doctoral Dissertation, University of Colorado. Accessed January 17, 2021. https://scholar.colorado.edu/asen_gradetds/167.

MLA Handbook (7^th Edition):

Dunham, Benjamin Zane. “High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices.” 2017. Web. 17 Jan 2021.

Vancouver:

Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2021 Jan 17]. Available from: https://scholar.colorado.edu/asen_gradetds/167.

Council of Science Editors:

Dunham BZ. High-Order Automatic Differentiation of Unmodified Linear Algebra Routines via Nilpotent Matrices. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/asen_gradetds/167

19. LI, XIAO. INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION.

Degree: MSc, 2017, McMaster University

URL: http://hdl.handle.net/11375/22521

►

We propose two efficient automatic differentiation (AD) schemes to compute incrementally Taylor series and System Jacobian for solving differential-algebraic equations (DAEs) by Taylor series. Our… (more)

Subjects/Keywords: Automatic Differentiation; Differential-Algebraic Equations; Common Subexpression Elimination; Taylor Series

…hand side) via automatic differentiation (AD) to form the underlying linear… …efficient evaluations of J and TCs in b using automatic differentiation. 10 CHAPTER 2… …common subexpressions during automatic differentiation. For all the examples in Chapter 4 and… …subexpressions by hand, if the differentiation is automated (which should be the case in practical… …step before computing. All successive overloaded computing including automatic…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

LI, X. (2017). INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/22521

Chicago Manual of Style (16^th Edition):

LI, XIAO. “INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION.” 2017. Masters Thesis, McMaster University. Accessed January 17, 2021. http://hdl.handle.net/11375/22521.

MLA Handbook (7^th Edition):

LI, XIAO. “INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION.” 2017. Web. 17 Jan 2021.

Vancouver:

LI X. INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION. [Internet] [Masters thesis]. McMaster University; 2017. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/11375/22521.

Council of Science Editors:

LI X. INCREMENTAL COMPUTATION OF TAYLOR SERIES AND SYSTEM JACOBIAN IN DAE SOLVING USING AUTOMATIC DIFFERENTIATION. [Masters Thesis]. McMaster University; 2017. Available from: http://hdl.handle.net/11375/22521

20. Hentz, Gauthier. Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design.

Degree: Docteur es, Robotique, 2017, Université de Strasbourg

URL: http://www.theses.fr/2017STRAD021

►

Dans le contexte médico-chirurgical, la robotique peut être d’un grand intérêt pour des procédures plus sûres et plus précises. Les contraintes d’encombrement sont cependant très… (more)

Subjects/Keywords: Conception de mécanismes; Espace de travail; Analyse de singularité; Continuation de haut-degré; Différentiation automatique; Sensibilité; Mechanism design; Workspace; Singularity analysis; Higher-order continuation; Automatic differentiation; Sensitivity; 629.89

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hentz, G. (2017). Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2017STRAD021

Chicago Manual of Style (16^th Edition):

Hentz, Gauthier. “Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design.” 2017. Doctoral Dissertation, Université de Strasbourg. Accessed January 17, 2021. http://www.theses.fr/2017STRAD021.

MLA Handbook (7^th Edition):

Hentz, Gauthier. “Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design.” 2017. Web. 17 Jan 2021.

Vancouver:

Hentz G. Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2017. [cited 2021 Jan 17]. Available from: http://www.theses.fr/2017STRAD021.

Council of Science Editors:

Hentz G. Outils numériques pour la conception de mécanismes : Numerical tools for mechanism design. [Doctoral Dissertation]. Université de Strasbourg; 2017. Available from: http://www.theses.fr/2017STRAD021

21. Martin, Nathan. Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology.

Degree: Docteur es, Mathematiques Appliquees, 2013, Toulouse, INSA

URL: http://www.theses.fr/2013ISAT0021

► Un certain nombre d’écoulements géophysiques, tels que les écoulements de glace ou de lave magmatique, impliquent le mouvement gravitaire à faible nombre de Reynolds d’un… (more)

▼ Un certain nombre d’écoulements géophysiques, tels que les écoulements de glace ou de lave magmatique, impliquent le mouvement gravitaire à faible nombre de Reynolds d’un fluide viscoplastique à surface libre sur un socle rocheux. Leur modélisation fait apparaître des lois de comportement rhéologique et des descriptions de leurs intéractions avec le socle rocheux qui reposent sur des paramétrisations empiriques. Par ailleurs, l’observation systématique de ce type d’écoulements avec une grande précision est rarement possible ; les données associées à l’observation de ces écoulements, principalement des données de surface (télédétections), peuvent être peu denses, manquantes ou incertaines. Elles sont aussi le plus souvent indirectes : des paramètres inconnus comme le glissement basal ou la rhéologie sont difficilement mesurables in situ.Ce travail de thèse s’attache à la modélisation directe et inverse de ces écoulements géophysiques, particulièrement les écoulements de glace, par des méthodes variationnelles à travers la résolution du problème de Stokes pour les fluides en loi de puissance.La méthode de résolution du problème direct (Stokes non-linéaire) repose sur le principe du minimum de dissipation qui mène à un problème variationnel de type point-selle à quatre champs pour lequel on montre l’existence de solutions. La condition d’incompressibilité et la loi de comportement représentent alors des contraintes associées au problème de minimisation. La recherche des points critiques du lagrangien correspondant est réalisée à l’aide d’un algorithme de type lagrangien augmenté, discrétisé par éléments finis triangles à trois champs. Cet algorithme conduit à un important gain tant en temps de calcul qu’en utilisation mémoire par rapport aux algorithmes classiques.On s’intéresse ensuite à la modélisation numérique inverse de ces fluides à l’aide du modèle adjoint et des deux principaux outils associés : l’analyse de sensibilité et l’assimilation de données. On étudie tout d’abord la modélisation rhéologique de ces fluides à travers les deux paramètres principaux de la loi de comportement : la consistance du fluide et l’exposant rhéologique. Des analyses de sensibilité sur ces paramètres définis localement, permettent de quantifier leurs poids relatifs au sein du modèle d’écoulement, en termes de vitesses de surface. L’identification de ces grandeurs est également réalisée. L’ensemble des résultats est résumé comme une méthodologie vers une “rhéométrie virtuelle” pouvant représenter une aide solide à la mesure rhéologique.Le glissement basal, paramètre majeur dans la dynamique de la glace, est investigué selon la même approche. Les analyses de sensibilité mettent en avant une capacité à voir à travers le caractère “filtré” et non-local de la transmission de la variabilité basale vers la surface, ouvrant des perspectives vers l’utilisation des sensibilités pour la définition de lieux d’intérêt pour l’observation et la mesure. Ce glissement basal, modélisation empirique d’un processus complexe et multiéchelle, est ensuite… Advisors/Committee Members: Monnier, Jérôme (thesis director).

Subjects/Keywords: Viscoplasticité; Éléments finis; Analyse de sensibilité variationnelle; Assimilation de données; Glaciologie; Lagrangien augmenté; Différentiation automatique; Viscoplasticity; Finite elements; Variational sensitivity analysis; Data assimilation; Glaciology; Augmented Lagrangian; Automatic differentiation; 532

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APA (6^th Edition):

Martin, N. (2013). Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology. (Doctoral Dissertation). Toulouse, INSA. Retrieved from http://www.theses.fr/2013ISAT0021

Chicago Manual of Style (16^th Edition):

Martin, Nathan. “Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology.” 2013. Doctoral Dissertation, Toulouse, INSA. Accessed January 17, 2021. http://www.theses.fr/2013ISAT0021.

MLA Handbook (7^th Edition):

Martin, Nathan. “Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology.” 2013. Web. 17 Jan 2021.

Vancouver:

Martin N. Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology. [Internet] [Doctoral dissertation]. Toulouse, INSA; 2013. [cited 2021 Jan 17]. Available from: http://www.theses.fr/2013ISAT0021.

Council of Science Editors:

Martin N. Modelisation directe et inverse d'ecoulements geophysiques viscoplastiques par methodes variationnelles : Application a la glaciologie : Direct and inverse modeling of viscoplastic geophysical flows using variational methods : Application to glaciology. [Doctoral Dissertation]. Toulouse, INSA; 2013. Available from: http://www.theses.fr/2013ISAT0021

22. Auliac, Sylvain. développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++.

Degree: Docteur es, Mathématiques, 2014, Université Pierre et Marie Curie – Paris VI

URL: http://www.theses.fr/2014PA066035

►

Cette thèse est consacrée au développement d'outils pour FreeFem++ destinés à faciliter la résolution des problèmes d'optimisation. Ce travail se compose de deux parties principales.… (more)

▼

Cette thèse est consacrée au développement d'outils pour FreeFem++ destinés à faciliter la résolution des problèmes d'optimisation. Ce travail se compose de deux parties principales. La première consiste en la programmation, la validation et l'exploitation d'interfaces permettant l¿utilisation de routines d'optimisation directement dans le logiciel. La seconde comprend le développement de solutions pour le calcul automatisé des dérivées, toujours au sein de FreeFem++, en exploitant les paradigmes de la différentiation automatique. FreeFem++ est un environnement de développement intégré dédié à la résolution numérique d¿équations aux dérivées partielles en dimension 2 et 3. Son langage ergonomique permet à l'utilisateur d'exploiter aisément ses nombreux outils de création de maillages, de résolution de systèmes linéaires, ainsi que ses bibliothèques d'éléments finis, etc... Nous introduisons les nouvelles routines d'optimisation désormais accessibles depuis la bibliothèque de modules du logiciel. En particulier, le logiciel libre d'optimisation sous contraintes IPOPT, qui implémente une méthode de points intérieurs très robuste pour l¿optimisation en grande dimension. Nous appliquons avec succès ces algorithmes à une série de problèmes concrets parmi lesquels la résolution numérique de problèmes de sur- faces minimales, la simulation de condensats de Bose-Einstein, ou encore un problème de positionnement inverse en mécanique des fluides. Une version prototypique de FreeFem++ contenant les outils de différentiation automatique est présentée, après avoir exposé les principes fondamentaux de cette méthode de calcul de dérivées pour le calcul scientifique.

The goal of this Ph.D. thesis was the development of tools for the FreeFem++ software in order to make optimization problems easier to deal with. This has been accomplished following two main directions. Firstly, a set of optimization softwares is interfaced and validated before making use of them. Then, we analyse the field of automatic differentiation as a potential mean of simplification for the users. FreeFem++ is an integrated development environment dedicated to numerically solving partial differential equations. Its high level language allows the user for a comfortable experience while using its mesh generation capabilities, linear system solvers, as well as finite elements capabilities. We describe the newly available optimization features, with a certain emphasis on the open source software IPOPT, which implements a state of the art interior points method for large scale optimization. These optimization tools are then used in a set of quite successful applications, among which minimal surfaces, Bose-Einstein condensate simulation, and an inverse positioning problem in the context of computational fluid dynamics. Finally, after an introduction to the techniques of algorithmic differentiation, we also present an unstable prototype version of FreeFem++ including automatic differentiation features.

Advisors/Committee Members: Hecht, Frédéric (thesis director).

Subjects/Keywords: Calcul scientifique; Développement de logiciel; Différentiation automatique; Méthode des éléments finis; Équations aux dérivées partielles; Optimisation; Automatic differentiation; Finite elements method; 510

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APA (6^th Edition):

Auliac, S. (2014). développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++. (Doctoral Dissertation). Université Pierre et Marie Curie – Paris VI. Retrieved from http://www.theses.fr/2014PA066035

Chicago Manual of Style (16^th Edition):

Auliac, Sylvain. “développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++.” 2014. Doctoral Dissertation, Université Pierre et Marie Curie – Paris VI. Accessed January 17, 2021. http://www.theses.fr/2014PA066035.

MLA Handbook (7^th Edition):

Auliac, Sylvain. “développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++.” 2014. Web. 17 Jan 2021.

Vancouver:

Auliac S. développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++. [Internet] [Doctoral dissertation]. Université Pierre et Marie Curie – Paris VI; 2014. [cited 2021 Jan 17]. Available from: http://www.theses.fr/2014PA066035.

Council of Science Editors:

Auliac S. développement d'outils d'optimisation pour freefem++ : Optimization tools development for FreeFemm++. [Doctoral Dissertation]. Université Pierre et Marie Curie – Paris VI; 2014. Available from: http://www.theses.fr/2014PA066035

Georgia Tech

23. Takemiya, Tetsushi. Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization.

Degree: PhD, Aerospace Engineering, 2008, Georgia Tech

URL: http://hdl.handle.net/1853/26515

► In modern aerospace engineering, the physics-based computational design method is becoming more important. However, high-fidelity models require longer computational time, so the advantage of efficiency… (more)

▼ In modern aerospace engineering, the physics-based computational design method is becoming more important. However, high-fidelity models require longer computational time, so the advantage of efficiency is partially lost. This problem has been overcome with the development of the approximation management framework (AMF). In the AMF, objective and constraint functions of a low-fidelity model are scaled at a design point so that the scaled functions, referred to as gsurrogate functions, h match those of a high-fidelity model. Since scaling functions and the low-fidelity model constitutes surrogate functions, evaluating the surrogate functions is faster than evaluating the high-fidelity model. Therefore, in the optimization process of the AMF, the surrogate functions are used to obtain a new design point. However, the author found that 1) the AMF is very vulnerable when the computational analysis models have numerical noise, and that 2) the AMF terminates optimization prematurely when the optimization problems have constraints. In order to solve the first problem, automatic differentiation (AD) technique is applied. If derivatives are computed with the generated derivative code, they are analytical, and the computational time is independent of the number of design variables. However, if analysis models implement iterative computations such as computational fluid dynamics (CFD), computing derivatives through the AD requires a massive memory size. The author solved this deficiency by modifying the AD approach and developing a more efficient implementation with CFD. In order to solve the second problem, the governing equation of the trust region ratio is modified so that it can accept the violation of constraints within some tolerance. By accepting violations of constraints during the optimization process, the AMF can continue optimization without terminating immaturely and eventually find the true optimum design point. With these modifications, the AMF is referred to as gRobust AMF, h and it is applied to airfoil and wing designs using Euler CFD software. The proposed AD method computes derivatives more accurately and faster than the finite differentiation method, and the Robust AMF successfully optimizes shapes of the airfoil and the wing in a much shorter time than the sequential quadratic programming with only high-fidelity models. Advisors/Committee Members: Mavris, Dimitri (Committee Chair), Alley, Nicholas (Committee Member), Lakshmi, Sankar (Committee Member), Sriram, Rallabhandi (Committee Member), Stephen, Ruffin (Committee Member).

Subjects/Keywords: Optimization; Automatic differentiation; CFD; Aerodynamics; Design; Aerospace engineering; Computational fluid dynamics; Quadratic programming

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APA (6^th Edition):

Takemiya, T. (2008). Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/26515

Chicago Manual of Style (16^th Edition):

Takemiya, Tetsushi. “Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization.” 2008. Doctoral Dissertation, Georgia Tech. Accessed January 17, 2021. http://hdl.handle.net/1853/26515.

MLA Handbook (7^th Edition):

Takemiya, Tetsushi. “Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization.” 2008. Web. 17 Jan 2021.

Vancouver:

Takemiya T. Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization. [Internet] [Doctoral dissertation]. Georgia Tech; 2008. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/1853/26515.

Council of Science Editors:

Takemiya T. Aerodynamic design applying automatic differentiation and using robust variable fidelity optimization. [Doctoral Dissertation]. Georgia Tech; 2008. Available from: http://hdl.handle.net/1853/26515

Purdue University

24. Barrett, Daniel P. Learning in vision and robotics.

Degree: PhD, Electrical and Computer Engineering, 2016, Purdue University

URL: https://docs.lib.purdue.edu/open_access_dissertations/620

► I present my work on learning from video and robotic input. This is an important problem, with numerous potential applications. The use of machine… (more)

Subjects/Keywords: Applied sciences; Automatic differentiation; Computer vision; Robot language comprehension; Robotic language learning; Video action localization; Video action recognition; Artificial Intelligence and Robotics; Computer Sciences; Robotics

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APA (6^th Edition):

Barrett, D. P. (2016). Learning in vision and robotics. (Doctoral Dissertation). Purdue University. Retrieved from https://docs.lib.purdue.edu/open_access_dissertations/620

Chicago Manual of Style (16^th Edition):

Barrett, Daniel P. “Learning in vision and robotics.” 2016. Doctoral Dissertation, Purdue University. Accessed January 17, 2021. https://docs.lib.purdue.edu/open_access_dissertations/620.

MLA Handbook (7^th Edition):

Barrett, Daniel P. “Learning in vision and robotics.” 2016. Web. 17 Jan 2021.

Vancouver:

Barrett DP. Learning in vision and robotics. [Internet] [Doctoral dissertation]. Purdue University; 2016. [cited 2021 Jan 17]. Available from: https://docs.lib.purdue.edu/open_access_dissertations/620.

Council of Science Editors:

Barrett DP. Learning in vision and robotics. [Doctoral Dissertation]. Purdue University; 2016. Available from: https://docs.lib.purdue.edu/open_access_dissertations/620

Cornell University

25. Tien, Joseph. Optimization for Bursting Neural Models.

Degree: 2006, Cornell University

URL: http://hdl.handle.net/1813/3504

► This thesis concerns parameter estimation for bursting neural models. Parameter estimation for differential equations is a difficult task due to complicated objective function landscapes and… (more)

Subjects/Keywords: optimization; bursting; neural models; parameter estimation; preBotzinger; Hodgkin-Huxley; automatic differentiation; algorithmic differentiation; dynamical systems; differential equations

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APA (6^th Edition):

Tien, J. (2006). Optimization for Bursting Neural Models. (Thesis). Cornell University. Retrieved from http://hdl.handle.net/1813/3504

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Tien, Joseph. “Optimization for Bursting Neural Models.” 2006. Thesis, Cornell University. Accessed January 17, 2021. http://hdl.handle.net/1813/3504.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Tien, Joseph. “Optimization for Bursting Neural Models.” 2006. Web. 17 Jan 2021.

Vancouver:

Tien J. Optimization for Bursting Neural Models. [Internet] [Thesis]. Cornell University; 2006. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/1813/3504.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Tien J. Optimization for Bursting Neural Models. [Thesis]. Cornell University; 2006. Available from: http://hdl.handle.net/1813/3504

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

26. Zhou, An. Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations.

Degree: 2017, University of Waterloo

URL: http://hdl.handle.net/10012/11183

► In many practical large scale computational problems, the calculation of partial derivatives of the object function f with respect to input parameters are entailed and… (more)

Subjects/Keywords: Automatic Differentiation; Reverse Mode; Structured Reverse Mode; Variable Annuities; Monte Carlo Simulations

…entailed. In such scenarios, reverse mode automatic differentiation (AD) becomes the… …Reverse mode Automatic Differentiation AD calculates the derivatives exactly and automatically… …runtime ratio, regardless of number of inputs. In Griewank’s On Automatic Differentiation[3… …mode automatic differentiation and discusses how different uses of structure affect the… …approximation and is easy to implement. Automatic differentiation computes the exact derivatives of…

8 more images…

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APA (6^th Edition):

Zhou, A. (2017). Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/11183

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Zhou, An. “Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations.” 2017. Thesis, University of Waterloo. Accessed January 17, 2021. http://hdl.handle.net/10012/11183.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Zhou, An. “Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations.” 2017. Web. 17 Jan 2021.

Vancouver:

Zhou A. Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations. [Internet] [Thesis]. University of Waterloo; 2017. [cited 2021 Jan 17]. Available from: http://hdl.handle.net/10012/11183.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Zhou A. Structured Reverse Mode Automatic Differentiation in Nested Monte Carlo Simulations. [Thesis]. University of Waterloo; 2017. Available from: http://hdl.handle.net/10012/11183

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. Herrmann, Julien. Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel.

Degree: Docteur es, Informatique, 2015, Lyon, École normale supérieure

URL: http://www.theses.fr/2015ENSL1043

►

Dans cette thèse, nous nous sommes penchés d’un point de vue à la foisthéorique et pratique sur la conception d’algorithmes et detechniques d’ordonnancement adaptées aux… (more)

▼

Dans cette thèse, nous nous sommes penchés d’un point de vue à la foisthéorique et pratique sur la conception d’algorithmes et detechniques d’ordonnancement adaptées aux architectures complexes dessuperordinateurs modernes. Nous nous sommes en particulier intéressésà l’utilisation mémoire et la gestion des communications desalgorithmes pour le calcul haute performance (HPC). Nous avonsexploité l’hétérogénéité des superordinateurs modernes pour améliorerles performances du calcul matriciel. Nous avons étudié lapossibilité d’alterner intelligemment des étapes de factorisation LU(plus rapide) et des étapes de factorisation QR (plus stablenumériquement mais plus deux fois plus coûteuses) pour résoudre unsystème linéaire dense. Nous avons amélioré les performances desystèmes d’exécution dynamique à l’aide de pré-calculs statiquesprenants en compte l’ensemble du graphe de tâches de la factorisationCholesky ainsi que l’hétérogénéité de l’architecture. Nous noussommes intéressés à la complexité du problème d’ordonnancement degraphes de tâches utilisant de gros fichiers d’entrée et de sortiesur une architecture hétérogène avec deux types de ressources,utilisant chacune une mémoire spécifique. Nous avons conçu denombreuses heuristiques en temps polynomial pour la résolution deproblèmes généraux que l’on avait prouvés NP-complet aupréalable. Enfin, nous avons conçu des algorithmes optimaux pourordonnancer un graphe de différentiation automatique sur uneplateforme avec deux types de mémoire : une mémoire gratuite maislimitée et une mémoire coûteuse mais illimitée.

Throughout this thesis, we have designed memory-aware algorithms and scheduling techniques suitedfor modern memory architectures. We have shown special interest in improving the performance ofmatrix computations on multiple levels. At a high level, we have introduced new numerical algorithmsfor solving linear systems on large distributed platforms. Most of the time, these linear solvers rely onruntime systems to handle resources allocation and data management. We also focused on improving thedynamic schedulers embedded in these runtime systems by adding static information to their decisionprocess. We proposed new memory-aware dynamic heuristics to schedule workflows, that could beimplemented in such runtime systems.Altogether, we have dealt with multiple state-of-the-art factorization algorithms used to solve linearsystems, like the LU, QR and Cholesky factorizations. We targeted different platforms ranging frommulticore processors to distributed memory clusters, and worked with several reference runtime systemstailored for these architectures, such as P A RSEC and StarPU. On a theoretical side, we took specialcare of modelling convoluted hierarchical memory architectures. We have classified the problems thatare arising when dealing with these storage platforms. We have designed many efficient polynomial-timeheuristics on general problems that had been shown NP-complete beforehand.

Advisors/Committee Members: Robert, Yves (thesis director).

Subjects/Keywords: Ordonnancement multi-critère; Algorithmes numériques; Factorisation LU; Factorisation QR; Factorisation Cholesky; Calcul haute performance; Systèmes linéaires; Différentiation automatique; Scheduling; Numerical algorithms; LU factorization; QR factorization; Cholesky factorization; High performance computing; Linear systems; Automatic differentiation

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APA (6^th Edition):

Herrmann, J. (2015). Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel. (Doctoral Dissertation). Lyon, École normale supérieure. Retrieved from http://www.theses.fr/2015ENSL1043

Chicago Manual of Style (16^th Edition):

Herrmann, Julien. “Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel.” 2015. Doctoral Dissertation, Lyon, École normale supérieure. Accessed January 17, 2021. http://www.theses.fr/2015ENSL1043.

MLA Handbook (7^th Edition):

Herrmann, Julien. “Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel.” 2015. Web. 17 Jan 2021.

Vancouver:

Herrmann J. Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel. [Internet] [Doctoral dissertation]. Lyon, École normale supérieure; 2015. [cited 2021 Jan 17]. Available from: http://www.theses.fr/2015ENSL1043.

Council of Science Editors:

Herrmann J. Memory-aware Algorithms and Scheduling Techniques for Matrix Computattions : Algorithmes orientés mémoire et techniques d'ordonnancement pour le calcul matriciel. [Doctoral Dissertation]. Lyon, École normale supérieure; 2015. Available from: http://www.theses.fr/2015ENSL1043

28. Locatelli, Florent. Sédimentation des boues activées en système fermé : de l'investigation expérimentale à l'aide d'un transducteur ultrasonore à la modélisation 1 D, l'analyse de sensibilité et l'identification de paramètres : Activated sludge batch settling : from experimental investigation using an ultrasonic transducer to 1D modelling, sensitivity analysis and parameter identification.

Degree: Docteur es, Mécanique des fluides, 2015, Université de Strasbourg

URL: http://www.theses.fr/2015STRAD033

►

Ce travail porte sur l’étude expérimentale et la modélisation de la sédimentation des boues activées. Un pilote expérimental associant une colonne de sédimentation et un… (more)

▼

Ce travail porte sur l’étude expérimentale et la modélisation de la sédimentation des boues activées. Un pilote expérimental associant une colonne de sédimentation et un transducteur ultrasonore est proposé. Des profils de vitesse de sédimentation et de concentration en particules sont obtenus grâce à ce dispositif, ce qui permet de mieux comprendre les mécanismes de décantation des boues. Ces résultats sont utilisés afin de développer une approche numérique. Un modèle de sédimentation est construit en intégrant des fonctions expérimentales. Une méthodologie mettant en œuvre la différentiation automatique du modèle est ensuite élaborée et appliquée, d'une part, à l'analyse de sensibilité du modèle aux paramètres des fonctions utilisées et, d'autre part, à l'identification des valeurs de ces paramètres à l'aide des résultats expérimentaux. La conjonction des approches expérimentale et numérique proposées constitue un processus efficace pour le développement des modèles de sédimentation.

This work deals with the experimental investigation and modelling of activated sludge settling. An experimental setup combining a settling column and an ultrasonic transducer is proposed. Settling velocity and concentration profiles are obtained using this setup, allowing for a better understanding of the mechanisms of activated sludge settling. These results are applied to the development of a numerical approach. A settling model using experimental functions is built. A methodology based on the automatic differentiation of the model is developed. This methodology is used, on the one hand, to analyse the sensitivity of the results to the model parameters and, on the other hand, to identify the parameter values on the basis of experimental data. The combination of the proposed experimental and numerical methods yields an efficient process for the development of sedimentation models.

Advisors/Committee Members: Bekkour, Karim (thesis director).

Subjects/Keywords: Clarification secondaire; Sédimentation de zone; Compression; Expérimentation en laboratoire; Méthode ultrasonore non invasive; Modélisation numérique; Approche mécaniste; Différentiation automatique; Secondary clarification; Zone settling; Compression; Laboratory experimentation; Non-invasive ultrasonic method; Numerical modelling; Mechanistic approach; Automatic differentiation; 532.5; 620

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APA (6^th Edition):

Locatelli, F. (2015). Sédimentation des boues activées en système fermé : de l'investigation expérimentale à l'aide d'un transducteur ultrasonore à la modélisation 1 D, l'analyse de sensibilité et l'identification de paramètres : Activated sludge batch settling : from experimental investigation using an ultrasonic transducer to 1D modelling, sensitivity analysis and parameter identification. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2015STRAD033

Chicago Manual of Style (16^th Edition):

Locatelli, Florent. “Sédimentation des boues activées en système fermé : de l'investigation expérimentale à l'aide d'un transducteur ultrasonore à la modélisation 1 D, l'analyse de sensibilité et l'identification de paramètres : Activated sludge batch settling : from experimental investigation using an ultrasonic transducer to 1D modelling, sensitivity analysis and parameter identification.” 2015. Doctoral Dissertation, Université de Strasbourg. Accessed January 17, 2021. http://www.theses.fr/2015STRAD033.

MLA Handbook (7^th Edition):

Locatelli, Florent. “Sédimentation des boues activées en système fermé : de l'investigation expérimentale à l'aide d'un transducteur ultrasonore à la modélisation 1 D, l'analyse de sensibilité et l'identification de paramètres : Activated sludge batch settling : from experimental investigation using an ultrasonic transducer to 1D modelling, sensitivity analysis and parameter identification.” 2015. Web. 17 Jan 2021.

Vancouver:

Locatelli F. Sédimentation des boues activées en système fermé : de l'investigation expérimentale à l'aide d'un transducteur ultrasonore à la modélisation 1 D, l'analyse de sensibilité et l'identification de paramètres : Activated sludge batch settling : from experimental investigation using an ultrasonic transducer to 1D modelling, sensitivity analysis and parameter identification. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2015. [cited 2021 Jan 17]. Available from: http://www.theses.fr/2015STRAD033.

Council of Science Editors:

Locatelli F. Sédimentation des boues activées en système fermé : de l'investigation expérimentale à l'aide d'un transducteur ultrasonore à la modélisation 1 D, l'analyse de sensibilité et l'identification de paramètres : Activated sludge batch settling : from experimental investigation using an ultrasonic transducer to 1D modelling, sensitivity analysis and parameter identification. [Doctoral Dissertation]. Université de Strasbourg; 2015. Available from: http://www.theses.fr/2015STRAD033

29. Zhao, Ze. Stochastic volatility models with applications in finance.

Degree: PhD, Applied Mathematical and Computational Sciences, 2016, University of Iowa

URL: https://ir.uiowa.edu/etd/2306

► Derivative pricing, model calibration, and sensitivity analysis are the three main problems in financial modeling. The purpose of this study is to present an… (more)

Subjects/Keywords: automatic differentiation; calibration; derivative pricing; gradient-based method; heuristic optimization method; stochastic volatility; Applied Mathematics

…Chapter 4. Chapter 5 will introduce the powerful Automatic Differentiation (AD), which… …Differentiation . . . . . . . . . . . . . . . . . . . . . 5.2.1 Forward Mode vs Reverse Mode…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhao, Z. (2016). Stochastic volatility models with applications in finance. (Doctoral Dissertation). University of Iowa. Retrieved from https://ir.uiowa.edu/etd/2306

Chicago Manual of Style (16^th Edition):

Zhao, Ze. “Stochastic volatility models with applications in finance.” 2016. Doctoral Dissertation, University of Iowa. Accessed January 17, 2021. https://ir.uiowa.edu/etd/2306.

MLA Handbook (7^th Edition):

Zhao, Ze. “Stochastic volatility models with applications in finance.” 2016. Web. 17 Jan 2021.

Vancouver:

Zhao Z. Stochastic volatility models with applications in finance. [Internet] [Doctoral dissertation]. University of Iowa; 2016. [cited 2021 Jan 17]. Available from: https://ir.uiowa.edu/etd/2306.

Council of Science Editors:

Zhao Z. Stochastic volatility models with applications in finance. [Doctoral Dissertation]. University of Iowa; 2016. Available from: https://ir.uiowa.edu/etd/2306

Université de Lorraine

30. Kpeky, Fessal. Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures.

Degree: Docteur es, Sciences des matériaux, 2016, Université de Lorraine

URL: http://www.theses.fr/2016LORR0008

►

Cette thèse s’intéresse au développement d’éléments finis solide–coques dédiés à la modélisation de structures multicouches sollicitées en vibrations. En effet, la plupart des modèles multicouches… (more)

▼

Cette thèse s’intéresse au développement d’éléments finis solide–coques dédiés à la modélisation de structures multicouches sollicitées en vibrations. En effet, la plupart des modèles multicouches dans la littérature présentent des limitations dans certaines configurations géométriques et matérielles. Face à ce constat et dans un souci de proposer un outil moins coûteux en temps de calcul, nous avons proposé une approche basée sur le concept solide–coques. Il s’agit d’éléments finis tridimensionnels dont le comportement a été amélioré par l’Assumed Strain Method. Dans un premier temps, nous avons formulé le problème de vibrations de structures sandwichs à cœur viscoélastique. La dépendance en fréquence a ainsi été prise en compte en utilisant une loi constitutive complexe. Pour résoudre le problème discrétisé, la Méthode Asymptotique Numérique, couplée à l’homotopie, et utilisant l’approche DIAMANT, a été adoptée pour les excellents résultats qu’elle offre par rapport aux autres méthodes. Des tests ont permis de valider les modèles proposés et de montrer l’avantage par rapport aux éléments ayant la même cinématique. Poursuivant nos travaux, et dans un souci d’augmenter l’amortissement, nous nous sommes orientés vers un contrôle actif des vibrations. Pour ce faire, deux éléments finis piézoélectriques ont été formulés. Il s’agit des éléments SHB8PSE et SHB20E qui sont des extensions des éléments finis SHB8PS et SHB20, respectivement. Le couplage électromécanique a consisté en l’ajout d’un degré de liberté à chacun des nœuds des dits éléments. Quelques exemples en statique et en vibrations menés sur des structures multicouches allant de simples poutres aux structures présentant des non-linéarités géométriques ont permis de valider les éléments solide–coques proposés. Pour finir, une synthèse des acquis des chapitres 2 et 3 a permis de proposer une modélisation de structures multicouches comprenant des couches élastiques, viscoélastiques et piézoélectriques. À l’amortissement passif provenant du pouvoir amortissant des matériaux viscoélastiques, on ajoute un contrôle actif qui découle du courant électrique généré au cours de la déformation des couches piézoélectriques. Ainsi, un filtre a été installé entre les capteurs et actionneurs. Ce filtre permet d’amplifier ou d’atténuer le potentiel électrique généré dans le but de réduire les amplitudes de vibrations. Pour résoudre le problème résultant nous avons étendu le solveur utilisé au chapitre 2. Pour valider les modèles proposés, des tests de contrôle actif–passif ont été menés sur des structures plaques multicouches. Enfin, quelques lois de contrôle découlant de filtres ont permis de montrer comment cette procédure permet de réduire ou même d’éviter l’amplification des vibrations

This thesis deals with the development of solid–shell finite elements for vibration modeling of multilayer structures. Indeed, most of multilayer models in the literature show some limitations in certain geometric and material configurations. Considering these restrictions and in order to…

Advisors/Committee Members: Abed-Meraim, Farid (thesis director), Daya, El Mostafa (thesis director).

Subjects/Keywords: Éléments finis solide–coques; Méthode « Assumed Strain »; Structures multicouches; Vibrations; Viscoélasticité; Piézoélectricité; Amortissement passif; Contrôle actif; Différentiation Automatique; Méthode Asymptotique Numérique; Solid–shell finite elements; Assumed Strain Method; Multilayer structures; Vibrations; Viscoelasticity; Piezoelectricity; Passive damping; Active control; Automatic Differentiation; Asymptotic Numerical Method; 620.3; 620.112 48

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kpeky, F. (2016). Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures. (Doctoral Dissertation). Université de Lorraine. Retrieved from http://www.theses.fr/2016LORR0008

Chicago Manual of Style (16^th Edition):

Kpeky, Fessal. “Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures.” 2016. Doctoral Dissertation, Université de Lorraine. Accessed January 17, 2021. http://www.theses.fr/2016LORR0008.

MLA Handbook (7^th Edition):

Kpeky, Fessal. “Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures.” 2016. Web. 17 Jan 2021.

Vancouver:

Kpeky F. Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures. [Internet] [Doctoral dissertation]. Université de Lorraine; 2016. [cited 2021 Jan 17]. Available from: http://www.theses.fr/2016LORR0008.

Council of Science Editors:

Kpeky F. Formulation et modélisation des vibrations par éléments finis de type solide-coque : application aux structures sandwichs viscoélastiques et piézoélectriques : Formulation and modeling of vibrations using solid-shell finite elements : application to viscoelastic and piezoelectric sandwich structures. [Doctoral Dissertation]. Université de Lorraine; 2016. Available from: http://www.theses.fr/2016LORR0008

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