3GAS-PINNs Proposed to Improve Physics-Informed Neural Network Accuracy

Researchers have introduced 3GAS-PINNs (Gradient-Guided Gaussian Adaptive Sampling Physics-Informed Neural Networks) to tackle common challenges in physics-informed neural network architectures. The preprint was published on the arXiv repository.

Standard PINNs often face slow convergence and struggle to capture localized intermittent structures like shock waves and solitons due to uniform collocation point distributions. The proposed 3GAS-PINN framework combines a uniform probability distribution with a Gaussian-smoothed distribution derived from spatial gradients, focusing computational points on steep gradient regions while maintaining global constraints.

The approach was benchmarked on three challenging nonlinear problems: the one-dimensional forced Burgers equation, the Korteweg-de Vries (KdV) equation, and the nonlinear Schrödinger equation. Test results indicate that 3GAS-PINNs can effectively improve physical consistency and enhance numerical simulation accuracy by up to 14 times compared to baseline PINN models.