Improving Ensemble Filters with Flow Matching

arXiv:2609.28015 · stat.ML, cs.LG, math.DS, stat.ME · Submitted 2026-09-23 · Read on arXiv

stat.ML, cs.LG, math.DS, stat.ME

Submitted: 2026-09-23

Updated: 2026-09-23

Terminology

• Benchmark — 21× in this paper · explained in 2 episodes
• Data Assimilation — 21× in this paper · explained in 2 episodes
• Flow Matching — 17× in this paper · explained in 8 episodes
• Calibration — 12× in this paper · explained in 7 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Optimal Transport — 4× in this paper · explained in 5 episodes
• Adam — 3× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• 2-Wasserstein Distance — 1× in this paper · explained in 1 episode
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Dynamical regimes — 1× in this paper · explained in 2 episodes
• Empirical Coverage — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Layer Normalization
• Learning Probabilistic Filters with Strictly Proper Scoring Rules
• Closed-form conditional diffusion models for data assimilation
• Gaussian Error Linear Units (GELUs)
• Flow Matching for Efficient and Scalable Data Assimilation
• IEnSF: Iterative Ensemble Score Filter for Reducing Error in Posterior Score Estimation in Nonlinear Data Assimilation

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