# LD-EnSF: Synergizing Latent Dynamics with Ensemble Score Filters for Fast Data Assimilation with Sparse Observations

arXiv: https://arxiv.org/abs/2411.19305 · HTML: https://mlsanity.com/paper/2411.19305/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 72 references that are in the map.
- First posted on arXiv 28 Nov 2024.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Score-based Data Assimilation](https://mlsanity.com/paper/2306.10574/) (2023)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [DiffDA: a Diffusion Model for Weather-scale Data Assimilation](https://mlsanity.com/paper/2401.05932/) (2024)
- [Data-driven discovery of intrinsic dynamics](https://mlsanity.com/paper/2108.05928/) (2021)
- [An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems](https://mlsanity.com/paper/2309.00983/) (2023)
- [Latent Space Data Assimilation by using Deep Learning](https://mlsanity.com/paper/2104.00430/) (2021)
- [Generalised Latent Assimilation in Heterogeneous Reduced Spaces with Machine Learning Surrogate Models](https://mlsanity.com/paper/2204.03497/) (2022)
- [Latent-EnSF: A Latent Ensemble Score Filter for High-Dimensional Data Assimilation with Sparse Observation Data](https://mlsanity.com/paper/2409.00127/) (2024)
- [Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations](https://mlsanity.com/paper/2108.03561/) (2021)
- [Integrating Recurrent Neural Networks with Data Assimilation for Scalable Data-Driven State Estimation](https://mlsanity.com/paper/2109.12269/) (2021)
- [Derivative-enhanced Deep Operator Network](https://mlsanity.com/paper/2402.19242/) (2024)
- [Inverse Problems and Data Assimilation](https://mlsanity.com/paper/1810.06191/) (2018)
- [Reduced-Order Autodifferentiable Ensemble Kalman Filters](https://mlsanity.com/paper/2301.11961/) (2023)
- [Multimodal 4DVarNets for the reconstruction of sea surface dynamics from SST-SSH synergies](https://mlsanity.com/paper/2207.01372/) (2022)
- [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)
- [Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space](https://mlsanity.com/paper/2410.11382/) (2024)
- [Latent assimilation with implicit neural representations for unknown dynamics](https://mlsanity.com/paper/2309.09574/) (2023)
- [State-observation augmented diffusion model for nonlinear assimilation with unknown dynamics](https://mlsanity.com/paper/2407.21314/) (2024)
- [Nonlinear Assimilation via Score-based Sequential Langevin Sampling](https://mlsanity.com/paper/2411.13443/) (2024)

## Built on by (most cited first, 11 of 11)

- [Flow Matching for Efficient and Scalable Data Assimilation](https://mlsanity.com/paper/2508.13313/) (2025)
- [Variationally correct operator learning: Reduced basis neural operator with a posteriori error estimation](https://mlsanity.com/paper/2512.21319/) (2025)
- [LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamics](https://mlsanity.com/paper/2602.19406/) (2026)
- [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)
- [Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics](https://mlsanity.com/paper/2512.11090/) (2025)
- [Generative Model Proposal based Particle Filtering for Data Assimilation](https://mlsanity.com/paper/2607.01012/) (2026)
- [Ensemble Controlled-Flow Filtering for Implicit Data Assimilation](https://mlsanity.com/paper/2607.12975/) (2026)
- [TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing](https://mlsanity.com/paper/2608.26219/) (2026)
- [AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation](https://mlsanity.com/paper/2609.32411/) (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)
- [LD-EnFF: Latent-Dynamics Ensemble Flow Filtering for Data Assimilation with Sparse Observations](https://mlsanity.com/paper/2610.04034/) (2026)

## Abstract (arXiv)

Data assimilation techniques are crucial for accurately tracking complex dynamical systems by integrating observational data with numerical forecasts. Recently, score-based data assimilation methods emerged as powerful tools for high-dimensional and nonlinear data assimilation. However, these methods still incur substantial computational costs due to the need for expensive forward simulations. In this work, we propose LD-EnSF, a novel score-based data assimilation method that eliminates the need for full-space simulations by evolving dynamics directly in a compact latent space. Our method incorporates improved Latent Dynamics Networks (LDNets) to learn accurate surrogate dynamics and introduces a history-aware LSTM encoder to effectively process sparse and irregular observations. By operating entirely in the latent space, LD-EnSF achieves speedups orders of magnitude over existing methods while maintaining high accuracy and robustness. We demonstrate the effectiveness of LD-EnSF on several challenging high-dimensional benchmarks with highly sparse (in both space and time) and noisy observations.