PILIR: Physics-Informed Local Implicit Representation

2026-05-01

AI Summary

This work addresses the spectral bias in physics-informed neural networks (PINNs) caused by global parameter coupling by proposing a local implicit representation framework. The approach decomposes the physical domain into local latent variables defined over a learnable grid and synthesizes a continuous solution via a generative neural operator. By breaking global coupling and enhancing spatial locality, the method effectively mitigates spectral bias, significantly improving both the reconstruction accuracy of high-frequency components and convergence speed across a range of complex partial differential equations. Experimental results demonstrate superior performance compared to current state-of-the-art methods.

Abstract

Physics-Informed Neural Networks have become a powerful mesh-free method for solving partial differential equations, but their performance is often limited by spectral bias. Specifically, in standard MLPs used in PINNs, the global parameter coupling causes the model to prioritize learning low-frequency components, resulting in slow convergence for high-frequency details. To overcome this limitation, we introduce the Physics-Informed Local Implicit Representation (PILIR). Our approach separates the global physical domain into a discrete latent feature space and a continuous generative decoder. By using a learnable grid to encode explicit spatial locality, PILIR can capture high-frequency details locally, preventing dilution by global patterns. A generative neural operator then synthesizes these local latent features into continuous physical fields, allowing accurate reconstruction of fine-scale structures. Experiments on a range of challenging PDEs show that PILIR effectively mitigates spectral bias, thereby boosting the convergence of high-frequency details and achieving superior accuracy compared to state-of-the-art methods.

Problem

• spectral bias
• Physics-Informed Neural Networks
• high-frequency details
• global parameter coupling
• partial differential equations

Innovation

• Physics-Informed Neural Networks
• Spectral Bias
• Local Implicit Representation
• Neural Operator
• High-Frequency Reconstruction