# LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamics

arXiv: https://arxiv.org/abs/2602.19406 · HTML: https://mlsanity.com/paper/2602.19406/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 23 Feb 2026.

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

- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation](https://mlsanity.com/paper/2504.18720/) (2025)
- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2411.19305/) (2024)

## Built on by (most cited first, 4 of 4)

- [Toward AI-Driven Digital Twins for Metropolitan Floods: A Conditional Latent Dynamics Network Surrogate of the Shallow Water Equations](https://mlsanity.com/paper/2605.13761/) (2026)
- [PR-Smoother: Simulator-Preserving Non-Gaussian Smoothing for Data Assimilation](https://mlsanity.com/paper/2609.26890/) (2026)
- [C-STRIDE: An Observation-Driven AI Digital Twin for Predicting Basin-Wide Flood Fields from Sparse Stream-Gauge Histories](https://mlsanity.com/paper/2609.39005/) (2026)
- [Learning PDE solution operators with variable initial conditions via Latent Dynamics Networks](https://mlsanity.com/paper/2610.08475/) (2026)

## Abstract (arXiv)

Long-range geophysical forecasts are fundamentally limited by chaotic dynamics and numerical errors. While data assimilation can mitigate these issues, classical variational smoothers require computationally expensive tangent-linear and adjoint models. Conversely, recent efficient latent filtering methods often enforce weak trajectory-level constraints and assume fixed observation grids. To bridge this gap, we propose Latent Ensemble Variational Data Assimilation (LEVDA), an ensemble-space variational smoother that operates in the low-dimensional latent space of a pretrained differentiable neural dynamics surrogate. By performing four-dimensional ensemble-variational (4DEnVar) optimization within an ensemble subspace, LEVDA jointly assimilates states and unknown parameters without the need for adjoint code or auxiliary observation-to-latent encoders. Leveraging the fully differentiable, continuous-in-time-and-space nature of the surrogate, LEVDA naturally accommodates highly irregular sampling at arbitrary spatiotemporal locations. Across three challenging geophysical benchmarks, LEVDA matches or outperforms state-of-the-art latent filtering baselines under severe observational sparsity while providing more reliable uncertainty quantification. Simultaneously, it achieves substantially improved assimilation accuracy and computational efficiency compared to full-state 4DEnVar.