Uncertainty-aware data assimilation through variational inference

2025/10/20 by Anthony Frion, Frion, Anthony, David S. Greenberg +1
Computer Science · Physics and Astronomy · #Adversarial Robustness in Machine Learning #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2510.17268

openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28

Abstract

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing deterministic machine learning approach, we propose a variational inference-based extension in which the predicted state follows a multivariate Gaussian distribution. Using the chaotic Lorenz-96 dynamics as a testing ground, we show that our new model enables to obtain nearly perfectly calibrated predictions, and can be integrated in a wider variational data assimilation pipeline in order to achieve greater benefit from increasing lengths of data assimilation windows. Our code is available at https://github.com/anthony-frion/Stochastic_CODA.

Citations

• Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations
• Score-based Data Assimilation
• Variational Data Assimilation with a Learned Inverse Observation Operator
• Combining data assimilation and machine learning to infer unresolved scale parametrisation
• Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles
• Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning
• Strictly Proper Scoring Rules, Prediction, and Estimation
• Accounting for an imperfect model in 4D‐Var
• A Practical Bayesian Framework for Backpropagation Networks

Related

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• On building the state error covariance from a state estimate