TY - JOUR
T1 - Hyper-parameter tuning of physics-informed neural networks
T2 - Application to Helmholtz problems
AU - Escapil-Inchauspé, Paul
AU - Ruz, Gonzalo A.
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
PY - 2023/12/7
Y1 - 2023/12/7
N2 - 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.
AB - 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.
KW - Bayesian optimization
KW - Helmholtz equation
KW - Hyper-parameter optimization
KW - Physics-informed neural networks
UR - http://www.scopus.com/inward/record.url?scp=85173236600&partnerID=8YFLogxK
U2 - 10.1016/j.neucom.2023.126826
DO - 10.1016/j.neucom.2023.126826
M3 - Article
AN - SCOPUS:85173236600
SN - 0925-2312
VL - 561
JO - Neurocomputing
JF - Neurocomputing
M1 - 126826
ER -