Deep Bayesian Filter for Bayes-faithful Data Assimilation

29 May 2024  ·  Yuta Tarumi, Keisuke Fukuda, Shin-ichi Maeda ·

State estimation for nonlinear state space models 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 state space models (SSMs). DBF constructs new latent variables $h_t$ on a new latent (``fancy'') space and assimilates observations $o_t$. By (i) constraining the state transition on fancy space to be linear and (ii) learning a Gaussian inverse observation operator $q(h_t|o_t)$, posteriors always remain Gaussian for DBF. Quite distinctively, the structured design of posteriors provides an analytic formula for the recursive computation of posteriors without accumulating Monte-Carlo sampling errors over time steps. DBF seeks the Gaussian inverse observation operators $q(h_t|o_t)$ and other latent SSM parameters (e.g., dynamics matrix) by maximizing the evidence lower bound. Experiments show that DBF outperforms model-based approaches and latent assimilation methods in various tasks and conditions.

PDF Abstract
No code implementations yet. Submit your code now

Tasks


Datasets


  Add Datasets introduced or used in this paper

Results from the Paper


  Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.

Methods


No methods listed for this paper. Add relevant methods here