Bayesian Filtering in Physical Systems via Test-time Trained Flow Matching

arXiv:2609.23383 · stat.ML, cs.AI, cs.LG · Submitted 2026-09-20 · Read on arXiv

stat.ML, cs.AI, cs.LG

Submitted: 2026-09-20

Updated: 2026-09-20

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Benchmark — 50× in this paper · explained in 2 episodes
• Flow Matching — 48× in this paper · explained in 8 episodes
• Transformer — 23× in this paper · explained in 2 episodes
• Generative Model — 16× in this paper · explained in 2 episodes
• Core — 13× in this paper · explained in 2 episodes
• Flow Matching Model — 12× in this paper · explained in 2 episodes
• Calibration — 10× in this paper · explained in 7 episodes
• Generative Models — 10× in this paper · explained in 2 episodes
• Test-Time Training — 10× in this paper
• Consistency — 7× in this paper · explained in 3 episodes
• Miscalibration Area — 7× in this paper
• Accuracy — 6× in this paper · explained in 1 episode
• Generalization — 6× in this paper · explained in 13 episodes
• Latent Space — 6× in this paper · explained in 7 episodes
• Amortization — 5× in this paper · explained in 1 episode
• Fidelity — 5× in this paper · explained in 2 episodes
• Ablation — 4× in this paper · explained in 1 episode
• Chaotic Dynamics — 4× in this paper · explained in 2 episodes
• Belief Flow Filter — 3× in this paper
• Downstream Tasks — 3× in this paper · explained in 2 episodes
• Fourier Neural Operator — 3× in this paper
• Inverse Problem — 3× in this paper · explained in 2 episodes
• Proper Orthogonal Decomposition — 3× in this paper
• Uncertainty Quantification — 3× in this paper · explained in 8 episodes
• Ablation study — 2× in this paper · explained in 1 episode
• Additive Decomposition — 2× in this paper · explained in 1 episode
• Anchor Noise — 2× in this paper · explained in 1 episode
• Classical Data Assimilation — 2× in this paper
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Diffusion Model — 2× in this paper · explained in 8 episodes
• Diffusion Models — 2× in this paper · explained in 6 episodes
• Extended Kalman Filter — 2× in this paper
• Generative Modeling — 2× in this paper · explained in 3 episodes
• Institutional Review Board — 2× in this paper
• Latent Representation — 2× in this paper · explained in 2 episodes
• Action Space — 1× in this paper · explained in 1 episode
• Active Exploration — 1× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Associative Memory — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Distribution Shift — 1× in this paper · explained in 5 episodes
• Empirical Coverage — 1× in this paper · explained in 2 episodes
• Exponential Moving Average (EMA) — 1× in this paper · explained in 2 episodes
• Information Gain — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Parsimony — 1× in this paper · explained in 2 episodes
• Reconstruction Error — 1× in this paper · explained in 2 episodes
• Rectified Flow — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Score Function — 1× in this paper · explained in 4 episodes
• Selection Bias — 1× in this paper · explained in 4 episodes
• Signal-to-noise ratio (SNR) — 1× in this paper · explained in 2 episodes
• Temporal Correlations — 1× in this paper · explained in 2 episodes
• Temporal consistency — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• U-net architecture — 1× in this paper · explained in 3 episodes
• Variational Bayes — 1× in this paper · explained in 2 episodes

Sources

• Uncertainty Toolbox: an Open-Source Library for Assessing, Visualizing, and Improving Uncertainty Quantification
• Flow Matching Guide and Code
• Lily Pad: Towards Real-time Interactive Computational Fluid Dynamics

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