Efficient Jacobian Determination by Structure-Revealing Automatic Differentiation

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;Combinatorics and Optimization

Xiong, Xin

University of Waterloo

关键词: 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;    Combinatorics and Optimization;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/8197/3/Xiong_Xin.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis is concerned with the efficient computation of Jacobian matrices of nonlinearvector maps using automatic differentiation (AD). Specifically, we propose the use oftwo 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.