Improved physics-informed neural network in mitigating gradient-related failures

Physics-informed neural network (PINN) integrates fundamental physical principles with advanced data driven techniques, leading to significant advancements in scientific computing. However, PINN encounters persistent challenges related to stiffness in gradient flow, which limits their predictive capabilities. This paper introduces an improved PINN (I-PINN) designed to mitigate gradient-related failures. The core of I-PINN combines the respective strengths of neural networks with an improved architecture and adaptive weights that include upper bounds. I-PINN achieves improved accuracy by at least one order of magnitude and accelerate convergence without introducing additional computational complexity compared to the baseline model. Numerical experiments across a variety of benchmarks demonstrate the enhanced accuracy and generalization of I-PINN. The supporting data and code are accessible at https://github.com/PanChengN/IPINN.git, facilitating broader research engagement.