{"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/picprop-physics-informed-confidence","title":"PICProp: Physics-Informed Confidence Propagation for Uncertainty Quantification","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"Standard approaches for uncertainty quantification in deep learning and physics-informed learning have persistent limitations. \nIndicatively, strong assumptions regarding the data likelihood are required, the performance highly depends on the selection of priors, and the posterior can be sampled only approximately, which leads to poor approximations because of the associated computational cost.\nThis paper introduces and studies confidence interval (CI) estimation for deterministic partial differential equations as a novel problem.\nThat is, to propagate confidence, in the form of CIs, from data locations to the entire domain with probabilistic guarantees.\nWe propose a method, termed Physics-Informed Confidence Propagation (PICProp), based on bi-level optimization to compute a valid CI without making heavy assumptions.\nWe provide a theorem regarding the validity of our method, and computational experiments, where the focus is on physics-informed learning. Code is available at https://github.com/ShenQianli/PICProp.Submission Number: 10991","url_abs":"https://openreview.net/forum?id=EETqXXdqkI","url_pdf":"https://openreview.net/pdf?id=EETqXXdqkI","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":"picprop-physics-informed-confidence","repo_url":"https://github.com/shenqianli/picprop","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[{"method_slug":"focus","method_name":"Focus"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}