New LIGO-PINN Method Improves Physics-Informed Neural Network Convergence

Physics-informed neural networks (PINNs) are powerful tools for modeling systems governed by partial differential equations (PDEs), but they often struggle with convergence failures, especially in complex PDE domains or when generalizing to new scenarios. Previous attempts to address these issues involved hyperparameter tuning, curriculum learning, or dynamic resampling of collocation points, each with its own limitations like high cost or ambiguity. This research highlights an under-investigated aspect: the initial weights of the PINN network. The authors propose a novel framework called Learned Initialization via Gated Layerwise Optimization (LIGO-PINN). This method focuses on optimizing the initial network weights to prevent catastrophic failures during training, offering a complementary approach to existing solutions. Extensive evaluations across 1D and 2D PDE domains, including a complex 2D fluid dynamics problem, demonstrate LIGO-PINN's superior performance. It achieved an average improvement of 91.5% over six baselines and 81% over the strongest existing method, also showing generalization to 3D unstructured domains. The study also analyzes training dynamics to explain why LIGO-PINN succeeds where traditional PINNs fail, making it a significant advancement for robust PDE modeling.