SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework

Bridging the gap between data-rich training regimes and observation-sparse deployment conditions remains a central challenge in spatiotemporal field reconstruction, particularly when target domains exhibit distributional shifts, heterogeneous structure, and multi-scale dynamics absent from available training data. We present SENDAI, a hierarchical $\textbf{S}$parse-measurement, $\textbf{E}$fficie$\textbf{N}$t $\textbf{D}$ata $\textbf{A}$ss$\textbf{I}$milation Framework that reconstructs full spatial states from hyper sparse sensor observations by combining simulation-derived priors with learned discrepancy corrections. We demonstrate the performance on satellite remote sensing, reconstructing MODIS (Moderate Resolution Imaging Spectroradiometer) derived vegetation index fields across six globally distributed sites. Using seasonal periods as a proxy for domain shift, the framework consistently outperforms established baselines that require substantially denser observations---SENDAI achieves a maximum SSIM improvement of 185% over traditional baselines and a 36% improvement over recent high-frequency-based methods. These gains are particularly pronounced for landscapes with sharp boundaries and sub-seasonal dynamics; more importantly, the framework effectively preserves diagnostically relevant structures---such as field topologies, land cover discontinuities, and spatial gradients. By yielding corrections that are more structurally and spectrally separable, the reconstructed fields are better suited for downstream inference of indirectly observed variables. The results therefore highlight a lightweight and operationally viable framework for sparse-measurement reconstruction that is applicable to physically grounded inference, resource-limited deployment, and real-time monitor and control.

Many important real-world systems - from ecosystems and climate to infrastructure and seismic activity - vary across space and over time, but we often cannot measure them everywhere. In Earth observation and other monitoring settings, sensors may be sparse, images may be blocked or incomplete, and collecting dense measurements can be expensive, slow, or impossible. This makes it hard to reconstruct the full picture. We present SENDAI, a lightweight data assimilation framework that reconstructs full spatial states from very sparse measurements. Instead of relying only on large training datasets or expensive computing, SENDAI combines what can be learned from data-rich reference examples with corrections learned from a small number of real observations. It also separates broad, smooth patterns from fine-scale details, helping preserve sharp boundaries and meaningful structures. We demonstrate SENDAI on satellite vegetation data, and also show that the same idea can extend to other kinds of spatial-temporal fields, including temperature, moisture, and seismic waves. This could support faster and more reliable monitoring in settings where measurements are limited, such as environmental management, disaster response, climate analysis, and remote or resource-constrained operations.