Pith Number

pith:W67CLRMD

pith:2023:W67CLRMD6WAOXPU43N7WLV57XL

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Bayesian Reasoning for Physics Informed Neural Networks

Kornel Witkowski, Krzysztof M. Graczyk

A Laplace approximation enables automatic optimization of loss weights in Bayesian physics-informed neural networks by computing model evidence analytically without sampling.

arxiv:2308.13222 v3 · 2023-08-25 · physics.comp-ph · cs.LG · physics.flu-dyn · stat.ML

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Claims

C1strongest 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.

C2weakest 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.

C3one line summary

Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.

References

75 extracted · 75 resolved · 9 Pith anchors

[1] Y. LeCun, Y. Bengio, G. Hinton, Deep learning , Nature 521 (2015) 436 EP –. URL https://doi.org/10.1038/nature14539 2015 · doi:10.1038/nature14539

[2] Day and Clint Richardson and Charles K 2019 · doi:10.1016/j.physrep.2019.03.001

[3] Neural Network Parameterizations of Electromagnetic Nucleon Form Factors 2010 · doi:10.1007/jhep09(2010)053

[4] The Proton Radius from Bayesian Inference 2014 · doi:10.1103/physrevc.90.054334

[5] K. M. Graczyk, M. Matyka, Predicting porosity, permeability, an d tortuosity of porous media from images by deep learning, Scientiﬁc reports 10 (1) (2020) 1–11 2020

Formal links

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Receipt and verification

First computed	2026-05-29T01:04:34.557437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7be25c583f580ebbe9cdb7f65d7bfbaf21006bdc7ea79efdcb8388d630470e4

Aliases

arxiv: 2308.13222 · arxiv_version: 2308.13222v3 · doi: 10.48550/arxiv.2308.13222 · pith_short_12: W67CLRMD6WAO · pith_short_16: W67CLRMD6WAOXPU4 · pith_short_8: W67CLRMD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W67CLRMD6WAOXPU43N7WLV57XL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b7be25c583f580ebbe9cdb7f65d7bfbaf21006bdc7ea79efdcb8388d630470e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3366fd83b32eabaa8be2ae0f5fc05fb9819698996b831ee9759702a089bbe98a",
    "cross_cats_sorted": [
      "cs.LG",
      "physics.flu-dyn",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2023-08-25T07:38:50Z",
    "title_canon_sha256": "93d0d2dccfd8da365eaacecdecb6fca6e5c62b842266d64b8b22ed978c126af5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.13222",
    "kind": "arxiv",
    "version": 3
  }
}