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

Paul Escapil-Inchauspé, Gonzalo A. Ruz

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider physics-informed neural networks (PINNs) (Raissiet al., 2019) 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 κ, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.

Original languageEnglish
Article number126826
StatePublished - 7 Dec 2023
Externally publishedYes


  • Bayesian optimization
  • Helmholtz equation
  • Hyper-parameter optimization
  • Physics-informed neural networks


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