mlsanityData to 7 Oct 2026

A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems

arXiv 2603.14863 ↗First posted 16 Mar 2026math.DS cs.LG math.PRcited by 3

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Abstract (arXiv)

We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecasting. Machine learning serves as an efficient numerical model for predicting dynamical systems. However, even with sufficient data, model uncertainty remains and accumulates over time, causing the long-term performance of ML models to deteriorate. To overcome this difficulty, we integrate data assimilation techniques into the training process to iteratively refine the model predictions by incorporating observational information. Specifically, we apply the Ensemble Score Filter (EnSF), a generative AI-based training-free diffusion model approach, for solving the data assimilation problem in high-dimensional nonlinear complex systems. This leads to a hybrid data assimilation-training framework that combines ML with EnSF to improve long-term predictive performance. We shall demonstrate that EnSF-enhanced ML can effectively reduce predictive uncertainty in ML-based Lorenz-96 system prediction and the Korteweg-De Vries (KdV) equation prediction.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 28 of its 83 references that are in the map. First posted on arXiv 16 Mar 2026.

Builds on

28 of 83 references.

References · 28

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16 more
  1. 2023PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEscited by 84
  2. 2024Operator Learning: Algorithms and Analysiscited by 84
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Generative Model Proposal based Particle Filtering for Data Assimilationcited by 0
  2. 2026FREESIA: Covariance-Aware Posterior Transport for Expressive and Scalable Data Assimilationcited by 0
  3. 2026AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilationcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026EnJoi: Ensemble Joint Score Filter for Generative Data Assimilation
  2. 2026Diffusion Model-Based Data Assimilation for Real-World Energy Consumption Forecasting
  3. 2024A competitive baseline for deep learning enhanced data assimilation using conditional Gaussian ensemble Kalman filtering
  4. 2025Flow Matching for Efficient and Scalable Data Assimilation
  5. 2026LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations
  6. 2025Training-Free Data Assimilation with GenCast
  7. 2026Closed-form conditional diffusion models for data assimilation
  8. 2025FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation