Physics-guided multi-well forecasting of uranium concentration in pregnant leach solutions from in-situ leaching wellfields: reducing hydrogeochemical peak-lag for process optimization

Hydrogeochemical response lag significantly complicates process control in uranium in-situ leaching (ISL), particularly within heterogeneous wellfields. To address this, a Physics-Guided State-Space Model (PG-SSM) is proposed to explicitly encode seven-spot topology and decouple fast operational signals from slow concentration dynamics. The model integrates soft physical regularizations to ensure hydrogeochemical plausibility. Evaluated on field data, PG-SSM achieves high accuracy (R ²  = 0.928, RMSE = 0.043 mg·L⁻¹) and reduces peak-timing lag to approximately + 1.5 days, significantly outperforming baselines. These results demonstrate that integrating topological priors and physical constraints effectively mitigates lag, providing a reliable basis for proactive ISL monitoring and control.