Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond
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.
| Comments: | 22 pages, 5 figures |
| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph) |
| MSC classes: | 68T07, 65D25, 65M06, 65N06 |
| ACM classes: | I.2.6; G.1.4; G.1.8 |
| Cite as: | arXiv:2608.11020 [cs.LG] |
| (or arXiv:2608.11020v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.11020
arXiv-issued DOI via DataCite (pending registration)
|
Submission history
From: Maciej J. Mikulski [view email][v1] Tue, 11 Aug 2026 15:01:29 UTC (522 KB)
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
Current browse context:
References & Citations
Bookmark
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
SLM-Conditioned Hierarchical Relation Routing for Labeled Property Graph Learning
Aug 28
-
NeuronFuzz: Safety Neuron Guided Fuzzing for LLM Safety Evaluation
Aug 28
-
Pruning Binarized Neural Networks: A Dedicated Framework and Globally Weighted Algorithms
Aug 28
-
Muon with Finite Newton-Schulz: The Smoothing Benefit in Nonsmooth Nonconvex Optimization
Aug 28
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.