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

• URL: http://arxiv.org/abs/2304.03552v2
• Date: Mon, 21 Oct 2024 10:29:32 GMT
• Title: A physics-informed neural network framework for modeling obstacle-related equations
• Authors: Hamid El Bahja, Jan Christian Hauffen, Peter Jung, Bubacarr Bah, Issa Karambal,
• Abstract summary: Physics-informed neural networks (PINNs) are an attractive tool for solving partial differential equations based on sparse and noisy data. Here we extend PINNs to solve obstacle-related PDEs which present a great computational challenge. The performance of the proposed PINNs is demonstrated in multiple scenarios for linear and nonlinear PDEs subject to regular and irregular obstacles.
• Score: 3.687313790402688
• License:
• 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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