Training-Free Bayesian Filtering with Generative Emulators

• URL: http://arxiv.org/abs/2605.20028v1
• Date: Tue, 19 May 2026 15:52:09 GMT
• Title: Training-Free Bayesian Filtering with Generative Emulators
• Abstract summary: We show that diffusion-based emulators of dynamical systems can be used to implement, without additional training, an optimal variant of particle filters.<n> Experiments on nonlinear chaotic systems, including atmospheric dynamics, demonstrate that the proposed approach successfully scales particle filtering to high-dimensional settings.
• Score: 8.157814461291746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian filtering is a well-known problem that aims to estimate plausible states of a dynamical system from observations. Among existing approaches to solve this problem, particle filters are theoretically exact for non-linear dynamics and observations, but suffer from poor scalability in high dimensions. In this work, we show that diffusion-based emulators of dynamical systems can be used to implement, without additional training, an optimal variant of particle filters that has remained largely unexplored due to implementation challenges with classical numerical solvers. Experiments on nonlinear chaotic systems, including atmospheric dynamics, demonstrate that the proposed approach successfully scales particle filtering to high-dimensional settings.

Related papers

• Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems [4.382988524355736]
  We propose a flow-based Bayesian filter (FBF) that integrates normalizing flows to construct a novel latent linear state-space model with Gaussian filtering distributions.<n>This framework facilitates efficient density estimation and sampling using invertible transformations provided by normalizing flows.<n> Numerical experiments demonstrate the superior accuracy and efficiency of FBF.
  arXiv  Detail & Related papers  (2025-02-22T14:04:23Z)
• Normalizing Flow-based Differentiable Particle Filters [16.164656853940464]
  We present a differentiable particle filtering framework that usesconditional normalizing flows to build its dynamic model, proposal distribution, and measurement model.<n>We derive the theoretical properties of the proposed filters and evaluate the proposed normalizing flow-based differentiable particle filters' performance through a series of numerical experiments.
  arXiv  Detail & Related papers  (2024-03-03T12:23:17Z)
• Closed-form Filtering for Non-linear Systems [83.91296397912218]
  We propose a new class of filters based on Gaussian PSD Models, which offer several advantages in terms of density approximation and computational efficiency. We show that filtering can be efficiently performed in closed form when transitions and observations are Gaussian PSD Models. Our proposed estimator enjoys strong theoretical guarantees, with estimation error that depends on the quality of the approximation and is adaptive to the regularity of the transition probabilities.
  arXiv  Detail & Related papers  (2024-02-15T08:51:49Z)
• Nonlinear Filtering with Brenier Optimal Transport Maps [6.048942663334447]
  This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a dynamical system.<n>Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states.<n>In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step.
  arXiv  Detail & Related papers  (2023-10-21T01:34:30Z)
• An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems [10.997994515823798]
  We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems. Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation. EnSF provides surprising performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter method.
  arXiv  Detail & Related papers  (2023-09-02T16:48:02Z)
• Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions [65.74069050283998]
  We propose a computational framework to approximate Doob's $h$-transforms. The proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters.
  arXiv  Detail & Related papers  (2022-06-07T15:03:05Z)
• Deep Learning for the Benes Filter [91.3755431537592]
  We present a new numerical method based on the mesh-free neural network representation of the density of the solution of the Benes model. We discuss the role of nonlinearity in the filtering model equations for the choice of the domain of the neural network.
  arXiv  Detail & Related papers  (2022-03-09T14:08:38Z)
• Deep Variational Models for Collaborative Filtering-based Recommender Systems [63.995130144110156]
  Deep learning provides accurate collaborative filtering models to improve recommender system results. Our proposed models apply the variational concept to injectity in the latent space of the deep architecture. Results show the superiority of the proposed approach in scenarios where the variational enrichment exceeds the injected noise effect.
  arXiv  Detail & Related papers  (2021-07-27T08:59:39Z)
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms [74.17312533172291]
  We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
  arXiv  Detail & Related papers  (2020-12-12T00:01:10Z)
• When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems? [60.703816720093016]
  This paper initiates a study on the efficiency of particle filtering for sequential planning. We are able to bound the number of particles needed so that the long-run reward of the policy based on particle filtering is close to that based on exact inference. We believe this technique can be useful in other sequential decision-making problems.
  arXiv  Detail & Related papers  (2020-06-10T17:43:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.