Generative point sampling strategies for physics-informed neural networks - Kochliaridis, Vasileios; Dilmperis, Ioannis; Palaskos, Achilleas; Vlahavas, Ioannis (Engineering with computers, 2025)
Physics-Informed Neural Networks (PINNs) have been a groundbreaking approach for solving complex boundary-value systems using Neural Networks. Although PINNs are capable of solving Partial Differential Equations (PDEs) relatively quickly, without having knowledge of the solution, their precision is still limited. One important factor that affects their efficiency is the selection of training points. To improve the sampling efficiency of the training data, we introduce Generative Point Sampling (GPS), a novel framework that incorporates advanced generative point sampling strategies to improve the effectiveness of PINNs. Our framework includes three innovative sampling methods: Genetic Sampling Strategy (GENESIS), Repetitive Epsilon-Greedy Sampling (REPS), and Generative Sampling using Reinforcement Learning (GENERAL). Each method is designed to optimize the distribution of the sampled training points in a way that enhances the learning process of PINNs. We conduct experiments on seven well-studied PDEs to evaluate the performance of our proposed methods against the previously established State-Of-The-Art method, named Residual-based Adaptive Refinement (RAR), presented in DeepXDE library. Our results demonstrate that all three GPS methods outperform RAR in terms of training efficiency, in most test cases.