Multimodal Physical Posterior Inference for Early Prediction of Surface Deformation from InSAR Time Series

Early observations of mining-induced subsidence reveal surface motion but leave its eventual magnitude and growth rate uncertain. This ambiguity makes forecasting from short interferometric synthetic aperture radar (InSAR) sequences difficult. We introduce Multimodal Physical Posterior Inference (MPPI), which uses geological and mining context to constrain physical parameters that early deformation maps cannot fully identify. MPPI combines visual patterns with textual descriptions of observation statistics and geological conditions to infer a posterior over maximum subsidence and growth rate. A physics-based decoder converts these parameters into future deformation fields and propagates posterior samples into prediction intervals. We pre-train the inference network on simulated sequences and fine-tune it on real InSAR observations. Across six coal-mining regions in Shanxi Province, China, MPPI achieves 4 cm RMSE for both maximum-subsidence estimation and deformation forecasting. Ablations identify geological information as the strongest complementary source, with textual representation providing further gains. Probabilistic parameter learning halves forecast RMSE relative to deterministic regression, while posterior sampling improves the continuous ranked probability score. These results support combining multimodal evidence with physical-parameter inference to forecast deformation from incomplete observations.