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Orientador(es)
Resumo(s)
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 meshbased 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.
Descrição
Palavras-chave
Physics-informed neural networks Fictitious domain method Irregular domains Steady-state heat conduction NURBS curves
Contexto Educativo
Citação
Rodrigues, J. A. (2025). Solving steady-state elliptic problems in irregular domains using physics-informed neural networks and fictitious domain methods. Research in Statistics, 3(1). https://doi.org/10.1080/27684520.2025.2542577
Editora
Taylor & Francis