Adversarial Adaptive Sampling for Physics-Informed Neural Network

In recent years, physically-informed neural networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs). However, vanilla PINNs encounter challenges when dealing with PDEs exhibiting multi-scale, chaotic, or turbulent behavior. In this study, we introduce an innovative method for improving PINNs by modifying the loss function to enable the model to accurately capture temporal causality during the training process. However, the observed effect did not yield the desired outcome in numerical experiments. Additionally, the quantity and spatial distribution of training data in the training process of PINNs will directly impact the efficacy of the model. Therefore, this study employs a projected gradient descent-based adversarial attack approach to dynamically select the training data, thereby bolstering the resilience of PINNs through fine-tuning the model with adversarial samples. We integrate pre-training with adaptive sampling using adversarial attacks. Pre-training aims to reduce the training time required for model training by breaking down a complex problem into several simpler ones. Effective pre-training in a shorter time frame can provide initial network parameter estimates and additional supervised learning datasets for training across the entire time domain.