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arXiv · 2409.09207

FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition

Milad Ramezankhani·Rishi Yash Parekh·Anirudh Deodhar·Dagnachew Birru
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Abstract

Deep operator networks (DeepONet) and neural operators have gained significant attention for their ability to map infinite-dimensional function spaces and perform zero-shot super-resolution. However, these models often require large datasets for effective training. While physics-informed operators offer a data-agnostic learning approach, they introduce additional training complexities and convergence issues, especially in highly nonlinear systems. To overcome these challenges, we introduce Finite Basis Physics-Informed HyperDeepONet (FB-HyDON), an advanced operator architecture featuring intrinsic domain decomposition. By leveraging hypernetworks and finite basis functions, FB-HyDON effectively mitigates the training limitations associated with existing physics-informed operator learning methods. We validated our approach on the high-frequency harmonic oscillator, Burgers' equation at different viscosity levels, and Allen-Cahn equation demonstrating substantial improvements over other operator learning models.

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Milad Ramezankhani, Rishi Yash Parekh, Anirudh Deodhar, Dagnachew Birru. 2024-09-13. FB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition. https://arxiv.org/abs/2409.09207

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