Architectural Insights for efficient Physics-Informed Neural Network optimization
Keywords: Physics informed neural networks (PINNs), optimization of physics informed neural networks, theoretical insights on PINNs
TL;DR: This paper provides theoretical and empirical contributions towards the optimization of physics informed neural networks, primarily from a neural architecture viewpoint.
Abstract: Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by combining deep learning with fundamental physics principles. Despite their remarkable empirical success, PINNs have garnered a reputation for their notorious training challenges across a spectrum of PDEs. In this work, we delve into the intricacies of PINN optimization from a neural architecture perspective. Leveraging the Neural Tangent Kernel (NTK), our study reveals that Gaussian activations surpass several alternate activations when it comes to effectively training PINNs. Building on insights from numerical linear algebra, we introduce a preconditioned neural architecture, showcasing how such tailored architectures enhance the optimization process. Our theoretical findings are substantiated through rigorous validation against established PDEs within the scientific literature.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 7402
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