A physics-informed neural network framework for modeling obstacle-related equations

2023/04/07 by Hamid El Bahja, Jan Christian Hauffen, Bahja, Hamid El +7 · 3 citations
Computer Science · Engineering · Physics and Astronomy · #Advanced Electrical Measurement Techniques #Analysis of PDEs (math.AP) #Computational Physics and Python Applications #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2304.03552

openalex publication_date 2023/04/07 · openalex created_date 2023/04/11 · openalex updated_date 2026/07/28

Abstract

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g., TensorFlow or PyTorch. Physics-informed neural networks (PINNs) are an attractive tool for solving partial differential equations based on sparse and noisy data. Here extend PINNs to solve obstacle-related PDEs which present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of the solution that lies above a given obstacle. The performance of the proposed PINNs is demonstrated in multiple scenarios for linear and nonlinear PDEs subject to regular and irregular obstacles.

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• A Hybrid Physics-Informed Neural Network Framework for Subcritical and Supercritical Dynamics in Multi-Species Chemotaxis
• A game-theoretic approach to the parabolic normalized p-Laplacian obstacle problem
• A deep first-order system least squares method for the obstacle problem

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