Solving Steady-State Elliptic Problems in Irregular Domains Using Physics-Informed Neural Networks and Fictitious Domain Methods
This paper introduces an innovative methodology for solving steady-state elliptic partial differential equations defined over irregular domains, by coupling the capabilities of Physics-Informed Neural Networks with the Fictitious Domain Method. The primary emphasis is placed on applications involvin...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis
2025-12-01
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| Series: | Research in Statistics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/27684520.2025.2542577 |
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| Summary: | This paper introduces an innovative methodology for solving steady-state elliptic partial differential equations defined over irregular domains, by coupling the capabilities of Physics-Informed Neural Networks with the Fictitious Domain Method. The primary emphasis is placed on applications involving the heat equation, a fundamental model in thermal analysis where the complexity of non-standard geometries often poses significant challenges for traditional numerical methods. The proposed approach exploits the inherent strength of Physics-Informed Neural Networks in embedding the underlying physical laws directly into the learning process, enabling the model to approximate solutions without relying on mesh-based discretization. Simultaneously, the Fictitious Domain Method facilitates the treatment of irregular computational domains by embedding them within a larger, regular domain, thereby simplifying the application of boundary conditions and numerical operations. The synergy between these two techniques results in a flexible, efficient, and accurate computational framework that is well-suited for addressing heat transfer problems in complex geometrical configurations. |
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| ISSN: | 2768-4520 |