Using Physics-Informed Neural Networks to Model the 2D Heat Equation
By Mihika Dusad, Michelle Kang, Emi Zhang, Laura Zhang
Partial differential equations (PDEs) are essential tools in various fields, but lack closed-form solutions, requiring approximation methods. Recent advancements like the Adomian domain decomposition method and the optimal auxiliary function method (OAFM) have improved PDE solution techniques, with OAFM offering linearization and efficient convergence in one interaction. Alongside mathematical approaches, computational tools like physics-informed neural networks (PINNs) have emerged, leveraging physics-based error terms for accuracy. Our project aims to integrate mathematical and computational methodologies to model the 2D heat equation, enhancing PINNs with classical analysis techniques and real-world data.
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