{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/hyper-parameter-tuning-of-physics-informed","title":"Hyper-parameter tuning of physics-informed neural networks: Application to Helmholtz problems","arxiv_id":"2205.06704","date":"2022-05-13","proceeding":null,"authors":["Paul Escapil-Inchauspé","Gonzalo A. Ruz"],"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.","url_abs":"https://arxiv.org/abs/2205.06704v2","url_pdf":"https://arxiv.org/pdf/2205.06704v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"hyper-parameter-tuning-of-physics-informed","repo_url":"https://github.com/pescap/hpomax","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"bayesian-optimization","task_name":"Bayesian Optimization"},{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[{"method_slug":"hpo","method_name":"HPO"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}