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arXiv Machine Learning By Lakshay Chawla, Hardik Jain

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

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LPINNs introduces a minimal modification to physics-informed neural networks (PINNs) by applying input‑dependent localization functions to the first hidden layer, creating receptive fields without domain partitioning. Across 13 localization families tested on a harmonic oscillator, a long‑interval heat equation, and a 4‑dimensional fourth‑order problem, three configurations—fixed Gaussian, inverse‑quadratic with learnable parameters, and fixed bump—significantly reduced solution error compared to the baseline. However, the benefit is not universal; many families performed worse, and only the inverse‑quadratic family consistently outperformed the baseline on all three equations.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

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