# Uncertainty-aware data assimilation through variational inference

arXiv: https://arxiv.org/abs/2510.17268 · HTML: https://mlsanity.com/paper/2510.17268/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [Combining data assimilation and machine learning to infer unresolved scale parametrisation](https://mlsanity.com/paper/2009.04318/) (2020)
- [Learning Variational Data Assimilation Models and Solvers](https://mlsanity.com/paper/2007.12941/) (2020)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [Combined Optimization of Dynamics and Assimilation with End-to-End Learning on Sparse Observations](https://mlsanity.com/paper/2409.07137/) (2024)

## Built on by (most cited first, 1 of 1)

- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)

## Abstract (arXiv)

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.