LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

2026-07-15

AI Summary

This work proposes LIGO-PINN, a learnable initialization framework based on gated layer-wise optimization, to address the persistent challenges of training instability and convergence to trivial solutions in physics-informed neural networks (PINNs) when solving complex partial differential equations (PDEs). For the first time, this study systematically investigates and leverages the impact of weight initialization on PINN training stability. By integrating physical constraints with deep learning optimization techniques, LIGO-PINN achieves stable and efficient training across one-, two-, and three-dimensional PDE problems without requiring costly hyperparameter tuning or curriculum learning. Experimental results demonstrate that LIGO-PINN improves average performance by 91.5% over six baseline methods and outperforms the strongest baseline by 81%, while exhibiting strong generalization capabilities in challenging scenarios such as 2D fluid dynamics and 3D unstructured domains.

Abstract

Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when generalizing to unseen but related PDE domains. Previously proposed solutions detail hyperparameter tuning to reduce loss imbalance between data-driven and physics guided losses, curriculum learning based training strategies, or dynamic re-sampling of hard collocation points. These methods face certain pitfalls: hyperparameter tuning is expensive, designing a training curriculum is ambiguous in multi-parameter PDE settings, and dynamic resampling still fails in complex PDE settings. Complementary to this line of thinking, we believe the initial PINN network weights also play a crucial role in the emergence of catastrophic failures during training, yet the effect of PINN weight initialization has been surprisingly under-investigated. To this end, we propose a framework for Learned Initialization via Gated Layerwise Optimization (LIGO-PINN) to overcome PINN convergence failures. Through rigorous evaluation on 1D and 2D PDE domains, including a challenging 2D fluid dynamics setting, we demonstrate that our methodology outperforms state-of-the-art methods designed to alleviate PINN failures, achieving a 91.5% average performance improvement across six baselines and 81% over the strongest baseline. We also verify that LIGO-PINN generalizes to 3D unstructured domains. Finally, we analyze training dynamics across all three PDE domains to explain both LIGO-PINN's improvement and the convergence failure of traditional PINNs. Code: https://github.com/scailab/ligo-pinn Keywords: Machine Learning, Physics-Informed Neural Networks, Deep Learning, PDE Modeling

Problem

• Physics-Informed Neural Networks
• Convergence Failure
• Partial Differential Equations
• Weight Initialization

Innovation

• Physics-Informed Neural Networks
• Learned Initialization
• Gated Optimization
• PDE Modeling
• Convergence Failure