arXiv:2506.12045v3 Announce Type: replace-cross Abstract: Much of the physical world is inaccessible to direct measurement and can be reached only through the sparse traces it leaves in other observable variables. Here we introduce the Temporal Radiation Operator Network (TRON), a spatiotemporal neural operator that learns proxy-to-field mappings, reconstructing otherwise unobserved physical fields from sparse, indirect sensor histories. For cosmic-radiation mapping, TRON reconstructs sea-level effective dose at 65,341 locations from histories of 12 neutron monitors, achieving 0.096\% mean relative $L_2$ error against EXPACS-generated reference fields in a chronologically held-out year; batched GPU inference evaluates a global field in approximately $\sim$1~ms, compared with $\sim$57.6~s for EXPACS on one CPU thread. On measured weather networks, TRON reconstructs temperature at held-out stations from thermometer or barometer histories, outperforming interpolation, calendar-based and hypsometric baselines. These results establish proxy-to-field reconstruction as a general route to recovering spatially distributed physical information beyond the direct reach of sparse sensor networks.