Batched Second-Order Adjoint Sensitivity for Reduced Space Methods

This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic differentiation (AutoDiff) backend that targets highly parallel ar...

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Bibliographic Details
Published in:arXiv.org 2022-01
Main Authors: Pacaud, François, Schanen, Michel, Maldonado, Daniel Adrian, Montoison, Alexis, Churavy, Valentin, Samaroo, Julian, Anitescu, Mihai
Format: Article
Language:English
Subjects:
Algorithms
Graphics processing units
Mathematical analysis
Nonlinear equations
Optimization
Sensitivity
Online Access:Get full text
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Summary:This paper presents an efficient method for extracting the second-order sensitivities from a system of implicit nonlinear equations on upcoming graphical processing units (GPU) dominated computer systems. We design a custom automatic differentiation (AutoDiff) backend that targets highly parallel architectures by extracting the second-order information in batch. When the nonlinear equations are associated to a reduced space optimization problem, we leverage the parallel reverse-mode accumulation in a batched adjoint-adjoint algorithm to compute efficiently the reduced Hessian of the problem. We apply the method to extract the reduced Hessian associated to the balance equations of a power network, and show on the largest instances that a parallel GPU implementation is 30 times faster than a sequential CPU reference based on UMFPACK.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.00241