A Lightweight Physics-Guided Dual-Target Neural Network for Cavern-Volume and Maximum-Radius Prediction in Solution-Mined Salt Caverns

Reliable prediction of final cavern responses is required for rapid screening of solution-mined salt caverns used in large-scale underground energy storage. Final cavern volume and maximum radius jointly control storage performance and geometric safety, but their simultaneous and physically consistent prediction remains challenging. In this study, a lightweight physics-guided neural network (LPGNN) was proposed for dual-target prediction of these two design-critical responses. The 25 recorded stage-wise construction variables were screened to retain 13 varying independent variables and are supplemented by five nonredundant process–geometric features describing leaching-time allocation, mean depth configuration, and staged depth adjustment. A shared residual encoder and two target-specific heads were trained using Huber loss and original-scale relative error for data fitting and a soft constraint related to source-defined cavern volume-coefficient consistency. The framework was evaluated using 1253 simulated five-stage solution-mining cases. On the independent test set, the LPGNN achieved mean absolute percentage error (MAPE) of 1.4779% for cavern volume and 2.8746% for maximum radius, with corresponding R2 values of 0.9506 and 0.8602, respectively. Correlation, Mantel-test, and feature-response analyses indicate that cavern volume is mainly associated with the overall leaching scale and vertical-control configuration, whereas maximum radius is more sensitive to staged depth adjustment and localized radial development. These results suggest that the proposed LPGNN can serve as an accurate and physically constrained surrogate for preliminary comparison and rapid screening of solution-mined salt-cavern construction schemes.