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LPINNs: First-Layer Gated Localization for Physics-Informed Neural Networks

arXiv · AI, language, vision and robotics · article · Sep 19, 2026 · UTC

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

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