{"paper":{"title":"Physics-informed neural particle flow for the Bayesian update step","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"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.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Domonkos Csuzdi, Oliv\\'er T\\\"or\\H{o}, Tam\\'as B\\'ecsi","submitted_at":"2026-02-26T15:10:45Z","abstract_excerpt":"The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff differential equations. Conversely, existing deep learning approximations typically treat the update as a black-box task or rely on asymptotic relaxation, neglecting the exact geometric structure of the finite-horizon probability transport. In this work, we propose a physics-informed neural particle flow, which is an amortized inference framework. To construct"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4260f894de20646b7ed81716b3fee7a0029f95ec060e27925edf27ad49f2233d"},"source":{"id":"2602.23089","kind":"arxiv","version":2},"verdict":{"id":"cc9afcba-9132-49ff-8e83-6b41ac304aaa","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T18:38:07.088699Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"references":{"count":72,"sample":[{"doi":"","year":2012,"title":"M.-H. Chen, Q.-M. Shao, J. G. Ibrahim, Monte Carlo methods in Bayesian computation, Springer Science & Business Media, 2012","work_id":"1658c9bd-131c-4b2e-aa5a-c1afaf297228","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"G. L. Jones, Q. Qin, Markov chain Monte Carlo in practice, Annual Review of Statistics and Its Application 9 (1) (2022) 557–578","work_id":"bb75bd6d-7a1d-48e7-942a-968bcfcc61ee","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"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","work_id":"306765d6-575a-49c1-872d-40abe85bd05d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1007/978-981-13-2971-5","year":2020,"title":"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","work_id":"94df91cb-83ef-4bea-93d6-08d7b65cbeb6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2004,"title":"C. P. Robert, G. Casella, Monte Carlo Statistical Methods, 2nd Edition, Springer, 2004","work_id":"3e9403b0-35ff-4ab7-8cf3-ca74dec4094f","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":72,"snapshot_sha256":"4f505a0a0855d09ae6a4d9d6f2ba7009f69ec87bb5ef10ac42a5ba852afadd26","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9af4963e6c4c4a8cdf9859597a694abe6ba437df6ce4cefe3495a0f2f9cbd04f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}