# Deep Bayesian Filter for Bayes-faithful Data Assimilation

arXiv: https://arxiv.org/abs/2405.18674 · HTML: https://mlsanity.com/paper/2405.18674/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 41 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 19 of 19)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [LaSOT: A High-quality Benchmark for Large-scale Single Object Tracking](https://mlsanity.com/paper/1809.07845/) (2018)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Deep Kalman Filters](https://mlsanity.com/paper/1511.05121/) (2015)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Dynamical Variational Autoencoders: A Comprehensive Review](https://mlsanity.com/paper/2008.12595/) (2020)
- [Sequential Neural Models with Stochastic Layers](https://mlsanity.com/paper/1605.07571/) (2016)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning](https://mlsanity.com/paper/1710.05741/) (2017)
- [Deep Learning for Day Forecasts from Sparse Observations](https://mlsanity.com/paper/2306.06079/) (2023)
- [Deep Latent State Space Models for Time-Series Generation](https://mlsanity.com/paper/2212.12749/) (2022)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [A multi-model ensemble Kalman filter for data assimilation and forecasting](https://mlsanity.com/paper/2202.02272/) (2022)

## Built on by (most cited first, 6 of 6)

- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)
- [Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems](https://mlsanity.com/paper/2502.16232/) (2025)
- [Amortized Filtering and Smoothing with Conditional Normalizing Flows](https://mlsanity.com/paper/2604.07169/) (2026)
- [TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing](https://mlsanity.com/paper/2608.26219/) (2026)
- [PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation](https://mlsanity.com/paper/2609.26890/) (2026)
- [LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2610.04034/) (2026)

## Abstract (arXiv)

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 ht in addition to the original physical variables zt and assimilates observations ot. By (i) constraining the state transition on the new latent space to be linear and (ii) learning a Gaussian inverse observation operator r(ht|ot), 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(ht|ot) 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.