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Title Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation
Publication Date
University/Publisher University of Waterloo
Abstract This thesis is concerned with the efficient computation of Jacobian matrices of nonlinear vector maps using automatic differentiation (AD). Specifically, we propose the use of two directed edge separator methods, the weighted minimum separator and natural order separator methods, to exploit the structure of the computational graph of the nonlinear system.This allows for the efficient determination of the Jacobian matrix using AD software. We will illustrate the promise of this approach with computational experiments.
Subjects/Keywords Automatic differentiation; Forward mode; Reverse mode; Directed acyclic graph; Computational graph; Directed edge separator; Jacobian matrix; Newton step; Minimum cutset; Ford-Fulkerson algorithm; Sparsity technique; Hidden structure
Language en
Country of Publication ca
Record ID handle:10012/8197
Repository waterloo
Date Retrieved
Date Indexed 2020-08-12

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…both ends of an edge is in G − S − T , assign 1 to it as its weight, otherwise assign infinity to it. The cutset found using 1-∞ weighting scheme is equivalent to the minimum-cut in G − S − T . In the case that S and T are adjacent or even overlapping…

…in G, we can similarly find another minimum-cut for G(S ∪ T ), and then combine it with the one in 20 G − S − T , to get a directed edge separator in G. A directed edge separator can then be generated from this edge cutset by algorihtm…

…6, 9, 3]T . We will use ADMAT[31] reverse mode to obtain J both directly and by constructing edge separators. Their running time and space usage will be recorded to see improvements. If cutset method is used, JE defined by equation…