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Uncertainty-aware data assimilation through variational inference

Anthony Frion, David S Greenberg

TL;DR

The paper addresses uncertainty in data assimilation by extending CODA to a probabilistic framework that outputs a diagonal Gaussian with mean $\boldsymbol{\mu}_t$ and covariance $\boldsymbol{\Sigma}_t$, trained via an unsupervised self-consistency objective using samples $\hat{\mathbf{x}}_t \sim \mathcal{N}(\boldsymbol{\mu}_t, \boldsymbol{\Sigma}_t)$ and horizon propagation. On the chaotic Lorenz-96 system, this approach yields nearly perfectly calibrated predictions, outperforming dropout and ensemble baselines as training data increases. The authors further integrate the trained stochastic CODA into a 4D-Var scheme by treating CODA outputs as priors, demonstrating improved data assimilation performance, particularly for longer windows and when observations are sparse. The work highlights a practical path to uncertainty-aware data assimilation via unsupervised probabilistic training and shows potential for scalable, stochastic extensions of classical variational methods.

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.

Uncertainty-aware data assimilation through variational inference

TL;DR

The paper addresses uncertainty in data assimilation by extending CODA to a probabilistic framework that outputs a diagonal Gaussian with mean and covariance , trained via an unsupervised self-consistency objective using samples and horizon propagation. On the chaotic Lorenz-96 system, this approach yields nearly perfectly calibrated predictions, outperforming dropout and ensemble baselines as training data increases. The authors further integrate the trained stochastic CODA into a 4D-Var scheme by treating CODA outputs as priors, demonstrating improved data assimilation performance, particularly for longer windows and when observations are sparse. The work highlights a practical path to uncertainty-aware data assimilation via unsupervised probabilistic training and shows potential for scalable, stochastic extensions of classical variational methods.

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.
Paper Structure (5 sections, 8 equations, 3 figures, 1 table)

This paper contains 5 sections, 8 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Variational CODA
  3. Training a stochastic CODA model
  4. Using a trained model for 4D-Var
  5. Conclusion

Figures (3)

  • Figure 1: Spread-skill plots for the variational, dropout and ensembling models, trained on the big dataset. The inset spread frequencies plot indicates the relative weights of the dots of the main plot when computing the SSREL. The 1:1 line represents a perfect calibration.
  • Figure 2: Mean squared error obtained by our 4 variants of 4D-Var, as a function of the assimilation window length. For each length, we use 10 different windows, and report the mean plus/minus standard deviation of the errors.
  • Figure 3: Visualization of a slice of an assimilation window with $T=10^5$ time steps. First row: ground truth state trajectory. Second row: Noisy and incomplete observations used in the 4D-Var cost. Third row: resulting predicted trajectory. Fourth row: differences between the predicted and true states.