A physics-informed neural network framework for modeling obstacle-related equations
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.
Cite
@article{arxiv.2304.03552,
title = {A physics-informed neural network framework for modeling obstacle-related equations},
author = {Hamid El Bahja and Jan Christian Hauffen and Peter Jung and Bubacarr Bah and Issa Karambal},
journal= {arXiv preprint arXiv:2304.03552},
year = {2024}
}