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.
@article{arxiv.2201.00241,
title = {Batched Second-Order Adjoint Sensitivity for Reduced Space Methods},
author = {François Pacaud and Michel Schanen and Daniel Adrian Maldonado and Alexis Montoison and Valentin Churavy and Julian Samaroo and Mihai Anitescu},
journal= {arXiv preprint arXiv:2201.00241},
year = {2022}
}