ObsConDA: Observability-Constrained Data Assimilation with Control-Space Inference

Irregular data assimilation is difficult because sparse, off-grid observations do not constrain the same state corrections from one cycle to the next. As the observation geometry changes, the set of supported correction directions changes as well. Many learning-based DA methods infer updates in a fixed latent or control space, even when the current observation layout supports a different set of correction directions. To address this mismatch, we introduce Observability-Constrained DataAssimilation with Control-Space Inference (ObsConDA), which determines those supported correction directions from the current background and observation geometry and infers only their control coefficients. On real surface-station assimilation, ObsConDA gives the best held-out station accuracy and the best full-field reconstruction among the tested classical and learned baselines. The same advantage carries to matched synthetic observations, explicit geometry shifts, and synthetic dynamical systems, supporting the view that the usable correction directions must change from cycle to cycle. Ablations show that the gain comes from adapting those directions themselves rather than from adding a latent corrector alone.