Deep Bayesian Filter for Bayes-faithful Data Assimilation

TL;DR

This paper introduces Deep Bayesian Filtering (DBF), a novel data assimilation method for nonlinear state space models that maintains Gaussian posteriors through a structured latent space, improving accuracy over traditional methods.

Contribution

DBF constructs a new latent space with linear dynamics and Gaussian inverse observation operators, enabling analytical recursive computation and better handling of non-Gaussian posteriors.

Findings

DBF outperforms existing model-based and latent methods in non-Gaussian scenarios.

DBF eliminates Monte Carlo sampling errors across time steps.

DBF effectively maintains Gaussian posteriors in complex nonlinear models.

Abstract

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.