The Ensemble Schr{ö}dinger Bridge filter for Nonlinear Data Assimilation

• URL: http://arxiv.org/abs/2512.18928v1
• Date: Mon, 22 Dec 2025 00:06:49 GMT
• Title: The Ensemble Schr{ö}dinger Bridge filter for Nonlinear Data Assimilation
• Authors: Feng Bao, Hui Sun,
• Abstract summary: This work puts forward a novel nonlinear optimal filter namely the Ensemble Schrdinger Bridge nonlinear filter.<n>The proposed filter finds marriage of the standard prediction procedure and the diffusion generative modeling for the analysis procedure to realize one filtering step.<n> Experimental results show that the designed algorithm performs well given highly nonlinear dynamics in (mildly) high dimension up to 40 or above under a chaotic environment.
• Score: 4.3169866624454345
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work puts forward a novel nonlinear optimal filter namely the Ensemble Schr{ö}dinger Bridge nonlinear filter. The proposed filter finds marriage of the standard prediction procedure and the diffusion generative modeling for the analysis procedure to realize one filtering step. The designed approach finds no structural model error, and it is derivative free, training free and highly parallizable. Experimental results show that the designed algorithm performs well given highly nonlinear dynamics in (mildly) high dimension up to 40 or above under a chaotic environment. It also shows better performance than classical methods such as the ensemble Kalman filter and the Particle filter in numerous tests given different level of nonlinearity. Future work will focus on extending the proposed approach to practical meteorological applications and establishing a rigorous convergence analysis.

Related papers

• An Efficient Conditional Score-based Filter for High Dimensional Nonlinear Filtering Problems [6.234365089734548]
  Conditional Score-based Filter (CSF) is a novel algorithm that leverages a set-transformer encoder and a conditional diffusion model to achieve efficient and accurate posterior sampling without retraining.<n> experiments on benchmark problems show that CSF achieves superior accuracy, robustness, and efficiency across diverse nonlinear filtering scenarios.
  arXiv  Detail & Related papers  (2025-09-24T06:55:52Z)
• 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)
• An Uncertainty Principle for Linear Recurrent Neural Networks [54.13281679205581]
  We build a linear filter of order $S$ that approximates the filter that looks $K$ time steps in the past.<n>We fully characterize the problem by providing lower bounds of approximation, as well as explicit filters that achieve this lower bound up to constants.<n>The optimal performance highlights an uncertainty principle: the filter has to average values around the $K$-th time step in the past with a range(width) that is proportional to $K/S$.
  arXiv  Detail & Related papers  (2025-02-13T13:01:46Z)
• Learning Optimal Filters Using Variational Inference [0.3749861135832072]
  We present a framework for learning a parameterized analysis map for filtering systems.<n>In principle this can lead to a better approximation of the filtering distribution, and hence smaller bias.<n>We show that this methodology can be used to learn the gain matrix, in an affine analysis map, for filtering linear and nonlinear dynamical systems.
  arXiv  Detail & Related papers  (2024-06-26T04:51:14Z)
• 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)
• Low-rank extended Kalman filtering for online learning of neural networks from streaming data [71.97861600347959]
  We propose an efficient online approximate Bayesian inference algorithm for estimating the parameters of a nonlinear function from a potentially non-stationary data stream. The method is based on the extended Kalman filter (EKF), but uses a novel low-rank plus diagonal decomposition of the posterior matrix. In contrast to methods based on variational inference, our method is fully deterministic, and does not require step-size tuning.
  arXiv  Detail & Related papers  (2023-05-31T03:48:49Z)
• 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)
• An energy-based deep splitting method for the nonlinear filtering problem [0.0]
  The main goal of this paper is to approximately solve the nonlinear filtering problem through deep learning. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network.
  arXiv  Detail & Related papers  (2022-03-31T16:26:54Z)
• 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)
• Unsharp Mask Guided Filtering [53.14430987860308]
  The goal of this paper is guided image filtering, which emphasizes the importance of structure transfer during filtering. We propose a new and simplified formulation of the guided filter inspired by unsharp masking. Our formulation enjoys a filtering prior to a low-pass filter and enables explicit structure transfer by estimating a single coefficient.
  arXiv  Detail & Related papers  (2021-06-02T19:15:34Z)

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.