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arXiv Machine Learning By Tak Shing Au Yeung, Ka Chun Cheung, Hannah Potgieter, Steven J. Ruuth, Simon See

Deep-Learning Solvers and Surrogates for Infinity and p-Laplace Problems

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The paper explores neural network solvers for infinity and p‑Laplace problems, employing Physics‑Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets). It addresses computational challenges for large p values (2 to 1000) across 2D and 3D domains, showing advantages over traditional mesh‑based solvers, especially in three dimensions. The authors provide conditional convergence results for PINNs, a universal approximation theorem for DeepONet on the parametric p‑Poisson problem, and validate their methods with numerical experiments comparing performance to conventional approaches.

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