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

Physics-Informed Neural Networks (PINNs) are powerful tools for solving partial differential equations (PDEs), but they frequently suffer from catastrophic training failures, often converging to trivial or inaccurate solutions in complex domains. While existing research focuses on loss balancing, curriculum learning, or adaptive sampling, these methods often struggle with generalization and require extensive hyperparameter tuning. This paper investigates whether the choice of initial network weights—a factor often overlooked in PINN literature—is a primary driver of these convergence failures.

The authors introduce LIGO-PINN (Learned Initialization via Gated Layerwise Optimization), a framework that replaces standard random weight initialization (e.g., Xavier or Kaiming) with weights learned through a meta-learning process. The framework consists of two main components:

1. Invariance Encoding (IE): A meta-learning procedure that trains the network on a distribution of 'easy' PDE configurations to distill invariant physical representations into the initial weights.
2. Gated Layerwise Optimization (GLO): A mechanism that controls the meta-update process by gradually 'unlocking' deeper layers of the network during training. This ensures that the initialization process focuses on stable, shallow representations before incorporating deeper, more complex dynamics.

LIGO-PINN was evaluated across 1D convection, 2D Helmholtz, and 2D incompressible Navier-Stokes equations. The results demonstrate that LIGO-PINN significantly outperforms state-of-the-art baselines, achieving an average performance improvement of 91.5% across six baselines and 81% over the strongest baseline. Qualitative analysis shows that while standard PINNs fail to capture complex features like vortex shedding in fluid dynamics, LIGO-PINN maintains high fidelity to analytical solutions. The authors also confirm that the learned initializations generalize effectively to 3D unstructured domains.