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

Physics-informed neural networks (PINNs) traditionally use a single shared representation across the entire computational domain, which can become challenging to optimize for long domains and high-order differential operators. LPINNs introduce a minimal modification by multiplying the first hidden layer activations of an otherwise standard dense PINN by input-dependent localization functions. This approach endows first-layer units with receptive fields without requiring domain partitioning or additional interface loss terms. The method provides a lightweight alternative for improving PINN optimization in complex physics problems.