Toward Principled Generative Data Assimilation of Turbulent Flows from Sparse Observations

Abstract

Turbulent flows are highly chaotic, which makes their instantaneous states difficult to predict. Data assimilation aims to reduce this predictive uncertainty by synthesizing the predictions of a physical solver with partial observations of the system. Traditional data assimilation methods such as ensemble and variational approaches can incur substantial computational cost through evaluations of high-fidelity solvers and, for variational methods, adjoint calculations. Recently, generative diffusion models have been explored in the solution of inverse problems in fluid mechanics, demonstrating their potential for data assimilation. However, existing diffusion-based methods often use free parameters instead of the prescribed observation-error covariance to control the balance between the prior and likelihood, departing from the Bayesian formulation of data assimilation. We propose a framework for principled generative data assimilation in which observations are assimilated in the clean-state space and the prescribed observation-error covariance enters explicitly through an ensemble Kalman update. In the Lorenz-63 system, the proposed method yields a lower trajectory error and equation residual than the other diffusion-based posterior sampling methods considered, although its ensemble underestimates the posterior uncertainty. In two-dimensional Rayleigh-Bénard convection, the generated fields recover the statistics of the direct numerical simulation reference at large scales, with deviations confined to the smaller scales. These results suggest that the framework can produce physically plausible turbulent flow fields, indicating its potential for more challenging turbulent flow applications.

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BibTeX RIS

BibTeX

@misc{turan2026toward,
  title = {{Toward Principled Generative Data Assimilation of Turbulent Flows from Sparse Observations}},
  author = {Baris Turan and Zhuoran Liu and Heng Xiao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37983},
  eprint = {2609.37983},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37983},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Toward Principled Generative Data Assimilation of Turbulent Flows from Sparse Observations
AU  - Baris Turan
AU  - Zhuoran Liu
AU  - Heng Xiao
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37983
UR  - https://arxiv.org/abs/2609.37983
AB  - Turbulent flows are highly chaotic, which makes their instantaneous states difficult to predict. Data assimilation aims to reduce this predictive uncertainty by synthesizing the predictions of a physical solver with partial observations of the system. Traditional data assimilation methods such as ensemble and variational approaches can incur substantial computational cost through evaluations of high-fidelity solvers and, for variational methods, adjoint calculations. Recently, generative diffusion models have been explored in the solution of inverse problems in fluid mechanics, demonstrating their potential for data assimilation. However, existing diffusion-based methods often use free parameters instead of the prescribed observation-error covariance to control the balance between the prior and likelihood, departing from the Bayesian formulation of data assimilation. We propose a framework for principled generative data assimilation in which observations are assimilated in the clean-state space and the prescribed observation-error covariance enters explicitly through an ensemble Kalman update. In the Lorenz-63 system, the proposed method yields a lower trajectory error and equation residual than the other diffusion-based posterior sampling methods considered, although its ensemble underestimates the posterior uncertainty. In two-dimensional Rayleigh-Bénard convection, the generated fields recover the statistics of the direct numerical simulation reference at large scales, with deviations confined to the smaller scales. These results suggest that the framework can produce physically plausible turbulent flow fields, indicating its potential for more challenging turbulent flow applications.
ER  -

Abstract

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