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

05/13/2022

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by   Paul Escapil-Inchauspé, et al.

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We consider physics-informed neural networks [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 tuning procedure via Gaussian processes-based Bayesian optimization. We apply the procedure to Helmholtz problems for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density r and (iii) the frequency κ, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.