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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.07765 |
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| _version_ | 1866917892212129792 |
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| author | Sobh, Nahil Gladstone, Rini Jasmine Meidani, Hadi |
| author_facet | Sobh, Nahil Gladstone, Rini Jasmine Meidani, Hadi |
| contents | Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PINN-FEM: A Hybrid Approach for Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks Sobh, Nahil Gladstone, Rini Jasmine Meidani, Hadi Machine Learning Computational Physics Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems. |
| title | PINN-FEM: A Hybrid Approach for Enforcing Dirichlet Boundary Conditions in Physics-Informed Neural Networks |
| topic | Machine Learning Computational Physics |
| url | https://arxiv.org/abs/2501.07765 |