LPINNs: First-Layer Gated Localization for Physics-Informed Neural Networks
Physics-informed neural networks (PINNs) use one shared representation over the computational domain, which can become difficult to optimize on long domains and for high-order operators. We study a minimal alternative: multiply the first hidden activation of an otherwise unchanged dense PINN by input-dependent localization functions, giving first-layer units receptive fields without partitioning the domain or adding interface losses. We screen 13 families of localization functions, in up to three parameterizations each, on a nonlinear harmonic oscillator (HO), a heat equation on a long spatial interval, and a manufactured four-dimensional (4D) fourth-order problem, with ten paired seeds t...
| Authors | Lakshay Chawla, Hardik Jain |
|---|---|
| Primary category | cs.LG |
| Published | 19 September 2026 |
| Last updated at source | 19 September 2026 |
Silytics shows public metadata from arXiv and links to the original. Information may be incomplete or out of date. Last refreshed 17 October 2026. Licenses and terms of the original apply to the work itself. Not financial, legal or professional advice.