Auxiliary Finite-Difference Residual-Gradient Regularization for PINNs
Physics-informed neural networks (PINNs) are often selected by a single scalar loss even when the quantity of interest is more specific. We study a hybrid design in which the governing PDE residual remains automatic-differentiation (AD) based, while finite differences (FD) appear only in a weak auxiliary term that penalizes gradients of the sampled residual field. The FD term regularizes the residual field without replacing the PDE residual itself. We examine this idea in two stages. Stage 1 is a controlled Poisson benchmark comparing a baseline PINN, the FD residual-gradient regularizer, and a matched AD residual-gradient baseline. Stage 2 transfers the same logic to a three-dimensional ...
| Authors | Stavros Kassinos |
|---|---|
| Primary category | cs.LG |
| Published | 15 April 2026 |
| Last updated at source | 15 April 2026 |
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