Deep Bayesian Filter for Bayes-faithful Data Assimilation
State estimation for nonlinear state space models (SSMs) is a challenging task. Existing assimilation methodologies predominantly assume Gaussian posteriors on physical space, where true posteriors become inevitably non-Gaussian. We propose Deep Bayesian Filtering (DBF) for data assimilation on nonlinear SSMs. DBF constructs new latent variables $h_t$ in addition to the original physical variables $z_t$ and assimilates observations $o_t$. By (i) constraining the state transition on the new latent space to be linear and (ii) learning a Gaussian inverse observation operator $r(h_t|o_t)$, posteriors remain Gaussian. Notably, the structured design of test distributions enables an analytical formula for the recursive computation, eliminating the accumulation of Monte Carlo sampling errors across time steps. DBF trains the Gaussian inverse observation operators $r(h_t|o_t)$ and other latent SSM parameters (e.g., dynamics matrix) by maximizing the evidence lower bound. Experiments demonstrate that DBF outperforms model-based approaches and latent assimilation methods in tasks where the true posterior distribution on physical space is significantly non-Gaussian.
Code (0)
등록된 구현이 없습니다.
Tasks
State EstimationState Space ModelsSimilar Papers 제목 키워드 기반
Flow Matching for Efficient and Scalable Data Assimilation
Data assimilation (DA) estimates a dynamical system's state from noisy observations. Recent generative models like the ensemble score filter (EnSF) improve DA in high-dimensional nonlinear settings but are computationall…
Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data
Accurate modeling and prediction of complex physical systems often rely on data assimilation techniques to correct errors inherent in model simulations. Traditional methods like the Ensemble Kalman Filter (EnKF) and its …
Weather ForecastingBI-EqNO: Generalized Approximate Bayesian Inference with an Equivariant Neural Operator Framework
Bayesian inference offers a robust framework for updating prior beliefs based on new data using Bayes' theorem, but exact inference is often computationally infeasible, necessitating approximate methods. Though widely us…
Bayesian InferenceGaussian ProcessesLearning Probabilistic Filters with Strictly Proper Scoring Rules
Bayesian filtering of partially and noisily observed dynamical systems seeks to infer the evolving conditional distribution of the state of a dynamical system, given observations, in an online fashion. This Bayesian filt…
Generative Model Proposal based Particle Filtering for Data Assimilation
Data assimilation models state dynamics conditioned on sequential observations, and has wide-ranging scientific applications. In the filtering setting, the goal is to model the posterior over the current state given all …