SAFE-Soil: Sparse anchor forecasting and field estimation for soil heating processes under limited monitoring

Subsurface soil heating is widely used in thermal remediation, yet internal monitoring is sparse and expensive, so operators rarely observe the future cold-side response or the evolving temperature field directly. Existing studies usually emphasize forward simulation or generic sequence forecasting, but they do not clearly assign different roles to sparse cold-point prediction and field reconstruction when well-control schedules are already known. To address this gap, we propose SAFE-Soil, a two-stage framework in which SAFE-Traj forecasts future cold-point temperatures from sparse histories and controls, while SAFE-Field combines a source-aware coarse prior with those predicted anchors to estimate future temperatures at arbitrary query locations. On the current sparse cold-point benchmark, the tuned SAFE-Traj branch reaches a mean test RMSE of 0.057 °C, compared with 0.079 °C for iTransformer-lite and 0.127 °C for PatchTST-lite, while remaining stable across five seeds. On the pooled full-point field benchmark, replacing weak future cues with SAFE-Traj anchors lowers SAFE-Field test MAE/RMSE from 24.269 °C/35.589 °C to 18.578 °C/29.990 °C, while the final system also outperforms the matched-budget and public field baselines retained in the main text. These results show that separating sparse trajectory forecasting from field-side correction gives a practical route for future thermal-field estimation under limited monitoring and offers a benchmark for further validation on broader real remediation data.