Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Deep Bayesian Filter for Bayes-Faithful Data Assimilation
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Proposes Deep Bayesian Filtering (DBF), a dynamical-VAE-style filter whose Gaussian inverse observation operator and linear latent dynamics give analytic recursive Gaussian filtering posteriors, trained by maximizing an ELBO.
Problem
Data assimilation in nonlinear state space models where filtering posteriors are non-Gaussian, and sampling-based filters (particle filters) and existing dynamical VAEs degrade or require nested Monte Carlo sampling.
Approach
Introduce latent variables h_t with linear Gaussian dynamics and a learned Gaussian inverse observation operator r(h_t|o_t), so the filtering posterior is Gaussian and computed analytically (Kalman-like recursion), with nonlinear emission phi mapping back to physical variables z_t.
Key results
- On two-body moving MNIST, DBF achieves 100% success (50/50) with position RMSE 0.39, while EnKF, ETKF and PF all reach 0% success.
- On Lorenz96 with nonlinear observations, DBF has RMSE 1.08 to 1.65 across noise levels, versus 2.97 or higher for the best baselines (KalmanNet, PFF, EnKF).
- On Lorenz96 with direct observation at sigma=1, EnKF (0.31) and ETKF (0.30) outperform DBF (0.53).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DBF instead of model-based filters | Two-body Moving MNIST assimilation · Two-body Moving MNIST | success rate: 0% (0/50) -> 100% (50/50) | Helped |
| Use DBF instead of the strongest baseline | Double pendulum assimilation · Double pendulum, σ=0.1, 0.3, 0.5 | RMSE θ: 0.04 \pm 0.01 -> 0.03 \pm 0.01; 0.06 \pm 0.02 -> 0.05 \pm 0.02; 0.08 \pm 0.04 -> 0.06 \pm 0.01 | Helped |
| Use DBF instead of the strongest baseline | Double pendulum assimilation · Double pendulum, σ=0.1, 0.3, 0.5 | RMSE ω: 0.33 \pm 0.07 -> 0.21 \pm 0.04; 0.35 \pm 0.14 -> 0.26 \pm 0.05; 0.40 \pm 0.16 -> 0.36 \pm 0.04 | Helped |
| Use DBF instead of ETKF | Double pendulum uncertainty estimation · Double pendulum, σ=0.1 | Jeffreys divergence: 0.12 -> 0.02 | Helped |
| Use DBF instead of EnKF or ETKF | Lorenz96 assimilation · Lorenz96 direct observation, σ=3 and σ=5 | RMSE: 0.83 -> 0.82; 1.73 -> 1.16 | Helped |
| Use DBF instead of EnKF | Lorenz96 assimilation · Lorenz96 nonlinear observation, σ=1, 3, 5 | RMSE: 4.69 -> 1.08; 3.93 -> 1.29; 3.81 -> 1.65 | Helped |
| Use DBF instead of ETKF | Lorenz96 assimilation · Lorenz96 direct observation, σ=1 | RMSE: 0.30 -> 0.53 | Hurt |
| Use squared rather than linear confidence to set observation covariance (ablation) | DBF object tracking · LaSOT airplane test videos | IoU | Helped |
Surprising findings
- DVAE baselines (DKF, VRNN, SRNN) and KalmanNet were unstable or failed to train in several settings, while DBF trained stably with eigenvalues near or below one.
- PDE-Refiner was excluded because it performed poorly with noisy observations.
Limitations
- Requires a training phase with paired physical/observation data or a pretrained Koopman operator, unlike model-based DA.
- Underperforms EnKF and ETKF in the low-noise direct-observation Lorenz96 setting (sigma=1).
- Gaussian posterior approximation introduces error when non-Gaussianity is weak.
Experimental setup
Datasets: moving MNIST double pendulum simulations Lorenz96 simulations LaSOT airplane videos
Benchmarks: two-body moving MNIST double pendulum Lorenz96 LaSOT airplane tracking
Metrics: RMSE success rate KL symmetric (Jeffreys divergence) IoU normalized precision
Baselines: EnKF ETKF particle filter PFF KalmanNet DKF VRNN SRNN
Builds on: Kalman filter Koopman operator variational autoencoder KalmanNet particle flow filter
Closest papers by meaning
- Predictively-Oriented Kalman Filtering (NeurIPS 2026 · similarity 0.88)
- Implicit Maximum a Posteriori Filtering via Adaptive Optimization (ICLR 2024 · similarity 0.87)
- Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data (ICLR 2025 · similarity 0.87)
- FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation (NeurIPS 2025 · similarity 0.87)
- Learning semilinear neural operators: A unified recursive framework for prediction and data assimilation. (ICLR 2024 · similarity 0.86)
- Gated Inference Network: Inference and Learning State-Space Models (NeurIPS 2024 · similarity 0.85)
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