# Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms

arXiv: https://arxiv.org/abs/2603.20891 · HTML: https://mlsanity.com/paper/2603.20891/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 20 of 20)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics](https://mlsanity.com/paper/2107.10043/) (2021)
- [Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model](https://mlsanity.com/paper/2001.01520/) (2020)
- [Using machine learning to correct model error in data assimilation and forecast applications](https://mlsanity.com/paper/2010.12605/) (2020)
- [A Framework for Machine Learning of Model Error in Dynamical Systems](https://mlsanity.com/paper/2107.06658/) (2021)
- [Auto-differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2107.07687/) (2021)
- [An overview of differentiable particle filters for data-adaptive sequential Bayesian inference](https://mlsanity.com/paper/2302.09639/) (2023)
- [Adaptively Truncating Backpropagation Through Time to Control Gradient Bias](https://mlsanity.com/paper/1905.07473/) (2019)
- [Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations](https://mlsanity.com/paper/2108.03561/) (2021)
- [Differentiable Particle Filtering without Modifying the Forward Pass](https://mlsanity.com/paper/2106.10314/) (2021)
- [Online learning of both state and dynamics using ensemble Kalman filters](https://mlsanity.com/paper/2006.03859/) (2020)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [Learning Enhanced Ensemble Filters](https://mlsanity.com/paper/2504.17836/) (2025)
- [Data Assimilation with Machine Learning Surrogate Models: A Case Study with FourCastNet](https://mlsanity.com/paper/2405.13180/) (2024)
- [Learning Optimal Filters Using Variational Inference](https://mlsanity.com/paper/2406.18066/) (2024)
- [Multimodal Atmospheric Super-Resolution With Deep Generative Models](https://mlsanity.com/paper/2506.22780/) (2025)
- [Non-Asymptotic Analysis of Ensemble Kalman Updates: Effective Dimension and Localization](https://mlsanity.com/paper/2208.03246/) (2022)
- [Machine Learning for Inverse Problems and Data Assimilation](https://mlsanity.com/paper/2410.10523/) (2024)
- [Reinforcement learning based data assimilation for unknown state model](https://mlsanity.com/paper/2511.02286/) (2025)

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

- [The Dynamic-Probabilistic Consistency Gap in Chaotic Surrogate Modeling](https://mlsanity.com/paper/2605.31547/) (2026)

## Abstract (arXiv)

Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics. This paper introduces a framework for jointly learning the state, dynamics, and parameters of filtering algorithms in data assimilation through a process we refer to as auto-differentiable filtering. The framework leverages a theoretically motivated loss function that enables learning from partial, noisy observations via gradient-based optimization using auto-differentiation. We further demonstrate how several well-known data assimilation methods can be learned or tuned within this framework. To underscore the versatility of auto-differentiable filtering, we perform experiments on dynamical systems spanning multiple scientific domains, such as the Clohessy-Wiltshire equations from aerospace engineering, the Lorenz-96 system from atmospheric science, and the generalized Lotka-Volterra equations from systems biology. Finally, we provide guidelines for practitioners to customize our framework according to their observation model, accuracy requirements, and computational budget.