Pith Number

pith:XXCVR527

pith:2026:XXCVR527NSOHCCAI6NMLDRMX5J

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Physics-informed neural particle flow for the Bayesian update step

Domonkos Csuzdi, Oliv\'er T\"or\H{o}, Tam\'as B\'ecsi

Coupling the log-homotopy path to the continuity equation produces a master PDE that a neural network solves unsupervised to transport prior densities to posteriors.

arxiv:2602.23089 v2 · 2026-02-26 · cs.LG

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Claims

C1strongest claim

By embedding this PDE as a physical constraint into the loss function, we train a neural network to approximate the transport velocity field. This approach enables purely unsupervised training, eliminating the need for ground-truth posterior samples.

C2weakest assumption

The log-homotopy trajectory of the prior to posterior density function can be coupled with the continuity equation to yield a well-posed master PDE whose solution is accurately approximated by a neural network without introducing new instabilities or bias.

C3one line summary

A neural network approximates the velocity field of log-homotopy particle flow by enforcing a derived master PDE from the continuity equation, enabling unsupervised amortized Bayesian updates with reduced stiffness.

References

72 extracted · 72 resolved · 1 Pith anchors

[1] M.-H. Chen, Q.-M. Shao, J. G. Ibrahim, Monte Carlo methods in Bayesian computation, Springer Science & Business Media, 2012 2012

[2] G. L. Jones, Q. Qin, Markov chain Monte Carlo in practice, Annual Review of Statistics and Its Application 9 (1) (2022) 557–578 2022

[3] S. Asmussen, P. W. Glynn, A new proof of convergence of MCMC via the ergodic theorem, Statistics & Proba- bility Letters 81 (10) (2011) 1482–1485 2011

[4] A. Barbu, S.-C. Zhu, Monte Carlo Methods, Springer Singapore, Singapore, 2020.doi:10.1007/ 978-981-13-2971-5. URLhttp://link.springer.com/10.1007/978-981-13-2971-5 2020 · doi:10.1007/978-981-13-2971-5

[5] C. P. Robert, G. Casella, Monte Carlo Statistical Methods, 2nd Edition, Springer, 2004 2004

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Cited by

1 paper in Pith

A Variational Lagrangian Framework for Log-Homotopy Particle Flow Filters

Receipt and verification

First computed	2026-05-18T02:45:05.099030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdc558f75f6c9c710808f358b1c597ea77321b6266f3af344da3d9cfa55924cb

Aliases

arxiv: 2602.23089 · arxiv_version: 2602.23089v2 · doi: 10.48550/arxiv.2602.23089 · pith_short_12: XXCVR527NSOH · pith_short_16: XXCVR527NSOHCCAI · pith_short_8: XXCVR527

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/XXCVR527NSOHCCAI6NMLDRMX5J \
  | 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: bdc558f75f6c9c710808f358b1c597ea77321b6266f3af344da3d9cfa55924cb

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
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    "submitted_at": "2026-02-26T15:10:45Z",
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