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arXiv · 2608.11020

Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond

Maciej J. Mikulski·Tadeusz Uhl
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Abstract

We systematically investigate finite-difference (FD) derivative computation in Physics-Informed Neural Networks (PINNs) as an alternative to automatic differentiation (AD). On three benchmark PDEs we show that, with a properly calibrated step size, FD matches AD in accuracy on every problem while running faster across the full tested batch-size range and using substantially less GPU memory, and that a stochastic variant we propose outperforms AD on a stationary problem. We further show that for neural architectures with inter-sample dependencies (e.g. BatchNorm, self-attention) the standard PyTorch autograd idiom is silently incorrect; the correct per-sample alternative is computationally infeasible at PINN-relevant batch sizes, while FD provides a forward-only approximation that is empirically an order of magnitude closer to the true per-sample derivative.

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BibTeXRIS

Maciej J. Mikulski, Tadeusz Uhl. 2026-08-11. Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond. https://arxiv.org/abs/2608.11020

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