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arXiv · 2103.09480

Hessian Chain Bracketing

Uwe Naumann·Shubhaditya Burela
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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.

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Uwe Naumann, Shubhaditya Burela. 2021-03-17. Hessian Chain Bracketing. https://arxiv.org/abs/2103.09480

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