The limits of exactness: On the failure of automatic differentiation in physics-informed machine learning
Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it the computational backbone of physics-informed machine learning. Yet exactness in the mathematical sense is not the same as fidelity to the physics. Here I argue that a derivative can be numerically perfect and still be the wrong derivative for the problem at hand, because AD, by construction, has no notion of the physical structure a solution must obey. Convection and its associated directionality, diffusion, and dispersion are only the most visible instances of a much longer list that spans all branches of computational science and engineeri...
| Authors | Ameya D. Jagtap |
|---|---|
| Primary category | cs.LG |
| Published | 27 September 2026 |
| Last updated at source | 30 September 2026 |
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