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arXiv · 2205.06704

Hyper-parameter tuning of physics-informed neural networks: Application to Helmholtz problems

Paul Escapil-Inchauspé·Gonzalo A. Ruz
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Abstract

We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO) procedure via Gaussian processes-based Bayesian optimization. We apply the HPO to Helmholtz equation for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density $r$ and (iii) the frequency $\kappa$, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.

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Paul Escapil-Inchauspé, Gonzalo A. Ruz. 2022-05-13. Hyper-parameter tuning of physics-informed neural networks: Application to Helmholtz problems. https://arxiv.org/abs/2205.06704

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