Where Should Observations Enter? Dual-Path Integration for Continuing Sensing with Recurrent Gaussian States

Reconstructing dense unsteady flow fields from sparse near-body measurements is an underdetermined inverse problem, as most of the field is never directly observed. A common latent-state design for sparse flow reconstruction compresses the available measurements into a single latent state and decodes every requested coordinate from that state. Although efficient for temporal propagation, this design couples state updating with query readout: when the latent state is the decoder's sole interface to the observations, every query is decoded from the same fused summary. This raises a central design question: should observations enter the recurrent state, the query readout, or both? GaussAssim addresses this question with two observation paths built around a recurrent anisotropic Gaussian field state. The state path assimilates observations into the Gaussian state for current decoding and subsequent propagation, while the query path uses time-indexed observation tokens to correct each readout without altering that state. On the ACDM Inc and periodic FlowBench benchmarks, GaussAssim outperforms the compared learned baselines in mean reconstruction error. Across four evaluation settings, ten-seed factorial comparisons show that each observation path further reduces mean error when the other is active. All eight conditional gains have pointwise 95% bootstrap intervals above zero. Equal-token controls on NURBS show that distinct past observations contribute beyond repeated current frames, while spatial diagnostics associate larger query corrections with higher state-only error. Together, these results demonstrate complementary benefits from recurrent state assimilation and direct query-conditioned observation access in continuing-sensing flow reconstruction.