Generative point sampling strategies for physics-informed neural networks

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...

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Bibliographic Details
Published in:Engineering with computers Vol. 41; no. 5; pp. 3219 - 3239
Main Authors: Kochliaridis, Vasileios, Dilmperis, Ioannis, Palaskos, Achilleas, Vlahavas, Ioannis
Format: Journal Article
Language:English
Published: London Springer London 01.10.2025
Springer Nature B.V
Subjects:
Boundary conditions
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer-Aided Engineering (CAD
Control
Deep learning
Efficiency
Finite volume method
Libraries
Machine learning
Math. Applications in Chemistry
Mathematical and Computational Engineering
Neural networks
Numerical analysis
Optimization algorithms
Original Article
Partial differential equations
Physics
R&D
Research & development
Sampling methods
Systems Theory
Generative modeling
Scientific computing
Computational science
Scientific machine learning
Physics-informed neural networks
Differential equations
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary: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.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-025-02158-4