# ADDA: a Modular Framework for Representing, Simulating and Assimilating Dynamics with End-to-end Differentiability arXiv: https://arxiv.org/abs/2608.23297 ยท HTML: https://mlsanity.com/paper/2608.23297/ ## Key facts - Cited by 1 papers in the map (data through 14 Oct 2026). - Builds on 48 of its 139 references that are in the map. - First posted on arXiv 24 Aug 2026. ## Builds on (most cited first, 30 of 48) - [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020) - [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021) - [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023) - [Machine learning with data assimilation and uncertainty quantification for dynamical systems: a review](https://mlsanity.com/paper/2303.10462/) (2023) - [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024) - [Learning Diffusion Priors from Observations by Expectation Maximization](https://mlsanity.com/paper/2405.13712/) (2024) - [TorchRL: A data-driven decision-making library for PyTorch](https://mlsanity.com/paper/2306.00577/) (2023) - [On conditional diffusion models for PDE simulations](https://mlsanity.com/paper/2410.16415/) (2024) - [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024) - [ACE2: Accurately learning subseasonal to decadal atmospheric variability and forced responses](https://mlsanity.com/paper/2411.11268/) (2024) - [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) - [JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows](https://mlsanity.com/paper/2203.13760/) (2022) - [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021) - [Deep Generative Data Assimilation in Multimodal Setting](https://mlsanity.com/paper/2404.06665/) (2024) - [Variational Data Assimilation with a Learned Inverse Observation Operator](https://mlsanity.com/paper/2102.11192/) (2021) - [Samudra: An AI Global Ocean Emulator for Climate](https://mlsanity.com/paper/2412.03795/) (2024) - [FengWu-4DVar: Coupling the Data-driven Weather Forecasting Model with 4D Variational Assimilation](https://mlsanity.com/paper/2312.12455/) (2023) - [Differentiable Programming for Earth System Modeling](https://mlsanity.com/paper/2208.13825/) (2022) - [Differentiable Programming for Differential Equations: A Review](https://mlsanity.com/paper/2406.09699/) (2024) - [Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation](https://mlsanity.com/paper/2109.12269/) (2021) - [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025) - [Fuxi-DA: A Generalized Deep Learning Data Assimilation Framework for Assimilating Satellite Observations](https://mlsanity.com/paper/2404.08522/) (2024) - [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025) - [Online learning of both state and dynamics using ensemble Kalman filters](https://mlsanity.com/paper/2006.03859/) (2020) - [4DVarNet-SSH: end-to-end learning of variational interpolation schemes for nadir and wide-swath satellite altimetry](https://mlsanity.com/paper/2211.05904/) (2022) - [Neural Koopman prior for data assimilation](https://mlsanity.com/paper/2309.05317/) (2023) - [Data Assimilation in the Latent Space of a Neural Network](https://mlsanity.com/paper/2012.12056/) (2020) - [AI enhanced data assimilation and uncertainty quantification applied to Geological Carbon Storage](https://mlsanity.com/paper/2402.06110/) (2024) - [Gradient-free online learning of subgrid-scale dynamics with neural emulators](https://mlsanity.com/paper/2310.19385/) (2023) ## Built on by (most cited first, 1 of 1) - [Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecasting](https://mlsanity.com/paper/2609.37435/) (2026) ## Abstract (arXiv) Data assimilation (DA) is an essential tool for prediction and understanding in the geosciences. DA combines simulation programs representing scientific knowledge with observations that constrain system dynamics, resulting in analyses and forecasts that incorporate both knowledge and data. DA tasks can be addressed with a diverse toolset, including variational, ensemble and learning-based methods. In particular, many recent works have proposed using automatic differentiation tools for variational, learning-based or hybrid methods. However, comprehensive comparisons across algorithms and dynamical systems remain challenging, due to the incompatibility of simulation and assimilation codes, inflexible handling of spatial and temporal discretizations, specialization of DA methods to specific simulations, and limited support for automatic differentiation and parallel computation in simulations. To address this challenge, we introduce Automatic Differentiation for Data Assimilation (ADDA), a software framework for defining and working with system states, simulations, observation schemes and DA methods. ADDA provides a powerful and flexible set of base classes for representing dynamical systems and observation operators, with support for collocated and staggered grids, unstructured meshes, Lagrangian state variables and irregular or continuous-time observations. Parallel processing and differentiability are first-class features, with support for batch axes and automatic differentiation throughout. ADDA is implemented in PyTorch library, but supports DA for JAX-based computation of dynamics and their gradients. To demonstrate its features, we further provide differentiable, ADDA-compatible implementations of 10 dynamical systems of various dimensionalities and scales, from which we design multiple illustrative DA examples. All of our code is publicly available at https://github.com/m-dml/ADDA.