{"paper":{"title":"Bayesian Reasoning for Physics Informed Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A Laplace approximation enables automatic optimization of loss weights in Bayesian physics-informed neural networks by computing model evidence analytically without sampling.","cross_cats":["cs.LG","physics.flu-dyn","stat.ML"],"primary_cat":"physics.comp-ph","authors_text":"Kornel Witkowski, Krzysztof M. Graczyk","submitted_at":"2023-08-25T07:38:50Z","abstract_excerpt":"We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN approaches based on sampling or variational inference, the proposed method uses a Laplace approximation to compute model evidence analytically, enabling efficient hyperparameter tuning and model comparison without posterior sampling. We demonstrate the method on the heat, wave, and Burgers' equations, obtaining solutions in agreement with exact or reference r"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data... the proposed method uses a Laplace approximation to compute model evidence analytically, enabling efficient hyperparameter tuning and model comparison without posterior sampling.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Laplace approximation around the posterior mode yields a sufficiently accurate estimate of the marginal likelihood (model evidence) for the purpose of loss-weight selection in PINN training; this premise is invoked when the authors state that the analytic evidence computation replaces sampling or variational inference.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Laplace approximation enables automatic optimization of loss weights in Bayesian physics-informed neural networks by computing model evidence analytically without sampling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dda765080efa5ed4685aeea84f1485b72bd8c6d1e8a58fd1461638cc81f93ca5"},"source":{"id":"2308.13222","kind":"arxiv","version":3},"verdict":{"id":"48ed7de6-9834-4a96-ba1e-12b1731b3b5d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T08:02:18.029728Z","strongest_claim":"We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data... the proposed method uses a Laplace approximation to compute model evidence analytically, enabling efficient hyperparameter tuning and model comparison without posterior sampling.","one_line_summary":"Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Laplace approximation around the posterior mode yields a sufficiently accurate estimate of the marginal likelihood (model evidence) for the purpose of loss-weight selection in PINN training; this premise is invoked when the authors state that the analytic evidence computation replaces sampling or variational inference.","pith_extraction_headline":"A Laplace approximation enables automatic optimization of loss weights in Bayesian physics-informed neural networks by computing model evidence analytically without sampling."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.13222/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":75,"sample":[{"doi":"10.1038/nature14539","year":2015,"title":"Y. 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