Hessian Chain Bracketing
Abstract
Second derivatives of mathematical models for real-world phenomena are fundamental ingredients of a wide range of numerical simulation methods including parameter sensitivity analysis, uncertainty quantification, nonlinear optimization and model calibration. The evaluation of such Hessians often dominates the overall computational effort. The combinatorial {\sc Hessian Accumulation} problem aiming to minimize the number of floating-point operations required for the computation of a Hessian turns out to be NP-complete. We propose a dynamic programming formulation for the solution of {\sc Hessian Accumulation} over a sub-search space. This approach yields improvements by factors of ten and higher over the state of the art based on second-order tangent and adjoint algorithmic differentiation.
Cite
@article{arxiv.2103.09480,
title = {Hessian Chain Bracketing},
author = {Uwe Naumann and Shubhaditya Burela},
journal= {arXiv preprint arXiv:2103.09480},
year = {2021}
}