Improved physics-informed neural network in mitigating gradient related failures

TL;DR

This paper introduces an improved physics-informed neural network (I-PINN) that effectively mitigates gradient-related failures, significantly enhancing accuracy and convergence speed without extra computational cost, demonstrated through various benchmarks.

Contribution

The paper proposes an enhanced architecture and adaptive weighting scheme for PINNs, addressing gradient stiffness issues and improving performance over baseline models.

Findings

I-PINN achieves at least one order of magnitude better accuracy.

I-PINN accelerates convergence without additional computational complexity.

Numerical experiments validate improved generalization of I-PINN.

Abstract

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in gradient flow, which limits their predictive capabilities. This paper presents an improved PINN (I-PINN) to mitigate gradient-related failures. The core of I-PINN is to combine the respective strengths of neural networks with an improved architecture and adaptive weights containingupper bounds. The capability to enhance accuracy by at least one order of magnitude and accelerate convergence, without introducing extra computational complexity relative to the baseline model, is achieved by I-PINN. Numerical experiments with a variety of benchmarks illustrate the improved accuracy and generalization of I-PINN. The supporting data and code are accessible at https://github.com/PanChengN/I-PINN.git, enabling broader research engagement.