LEVDA: Latent Ensemble Variational Data Assimilation via Differentiable Dynamics

TL;DR

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 and achieves substantially improved assimilation accuracy and computational efficiency compared to full-state 4DEnVar.

Abstract

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.

Figures (9)

• Figure 1: Relative RMSE of the ensemble-mean trajectory over time for Kolmogorov flow (left), tsunami modeling (middle), and atmospheric modeling (right); shaded regions show the standard deviation of member-wise relative RMSE.
• Figure 2: Atmospheric benchmark: final-time zonal wind $u$ at 500 hPa. The visualization compares the ground truth (with sparse observations) to the assimilated states and errors for different methods.
• Figure 3: Effect of irregular sampling on tsunami modeling: (a) moving observation locations (randomized at each observed time), (b) irregular observation times with fixed spatial locations, and (c) joint spatiotemporal irregularity. Curves depict the relative RMSE of the ensemble-mean trajectory; shaded regions indicate the standard deviation of member-wise relative RMSE.
• Figure 4: Tsunami benchmark sensitivity analysis: LEVDA Relative RMSE as a function of (a) smoothing time horizon $\tau$, (b) ensemble size $K$, and (c) spatial observation stride (sparsity).
• Figure 5: Additional Tsunami benchmark ablations: (a) Impact of temporal sparsity on LEVDA Relative RMSE (using extended smoothing window $\tau=10$). (b) Robustness to observation noise (5%, 10%, 20% noise-to-signal ratios) under fixed likelihood weighting. (c) Parameter estimation accuracy: Relative RMSE of the parameter $u$ over the assimilation window.