# TorchDA: A Python package for performing data assimilation with deep learning forward and transformation functions

arXiv: https://arxiv.org/abs/2409.00244 · HTML: https://mlsanity.com/paper/2409.00244/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 63 references that are in the map.
- First posted on arXiv 30 Aug 2024.

## Builds on (most cited first, 15 of 15)

- [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023)
- [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)
- [Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization](https://mlsanity.com/paper/2001.06270/) (2020)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation](https://mlsanity.com/paper/2109.12269/) (2021)
- [Attention-based Convolutional Autoencoders for 3D-Variational Data Assimilation](https://mlsanity.com/paper/2101.02121/) (2021)
- [Online model error correction with neural networks in the incremental 4D-Var framework](https://mlsanity.com/paper/2210.13817/) (2022)
- [Data Assimilation Networks](https://mlsanity.com/paper/2010.09694/) (2020)
- [Data Assimilation in the Latent Space of a Neural Network](https://mlsanity.com/paper/2012.12056/) (2020)
- [Enhancing State Estimation in Robots: A Data-Driven Approach with Differentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2308.09870/) (2023)
- [Low-rank Approximations for Computing Observation Impact in 4D-Var Data Assimilation](https://mlsanity.com/paper/1307.5076/) (2013)
- [A Novel Neural Network Training Framework with Data Assimilation](https://mlsanity.com/paper/2010.02626/) (2020)
- [Enable High-resolution, Real-time Ensemble Simulation and Data Assimilation of Flood Inundation using Distributed GPU Parallelization](https://mlsanity.com/paper/2302.08341/) (2023)

## Built on by (most cited first, 5 of 5)

- [Tensor-Var: Efficient Four-Dimensional Variational Data Assimilation](https://mlsanity.com/paper/2501.13312/) (2025)
- [Constrained Sensing and Reliable State Estimation with Shallow Recurrent Decoders on a TRIGA Mark II Reactor](https://mlsanity.com/paper/2510.12368/) (2025)
- [ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability](https://mlsanity.com/paper/2608.23297/) (2026)
- [pyforce-1.0.0: Python Framework for data-driven model Order Reduction of multi-physiCs problEms](https://mlsanity.com/paper/2605.18082/) (2026)
- [Variational Parameter Calibration with Physics-Aware Latent-Space Surrogates](https://mlsanity.com/paper/2608.11435/) (2026)

## Abstract (arXiv)

Data assimilation techniques are often confronted with challenges handling complex high dimensional physical systems, because high precision simulation in complex high dimensional physical systems is computationally expensive and the exact observation functions that can be applied in these systems are difficult to obtain. It prompts growing interest in integrating deep learning models within data assimilation workflows, but current software packages for data assimilation cannot handle deep learning models inside. This study presents a novel Python package seamlessly combining data assimilation with deep neural networks to serve as models for state transition and observation functions. The package, named TorchDA, implements Kalman Filter, Ensemble Kalman Filter (EnKF), 3D Variational (3DVar), and 4D Variational (4DVar) algorithms, allowing flexible algorithm selection based on application requirements. Comprehensive experiments conducted on the Lorenz 63 and a two-dimensional shallow water system demonstrate significantly enhanced performance over standalone model predictions without assimilation. The shallow water analysis validates data assimilation capabilities mapping between different physical quantity spaces in either full space or reduced order space. Overall, this innovative software package enables flexible integration of deep learning representations within data assimilation, conferring a versatile tool to tackle complex high dimensional dynamical systems across scientific domains.