A Generative Augmentation and Physics-Informed Network for Interpretable Prediction of Mining-Induced Deformation from InSAR Data

Accurate forecasting of mining-induced surface deformation is critical for coal-mine safety assessment and hazard mitigation. InSAR deformation time series are often short, temporally sparse, and strongly nonlinear. These characteristics can make purely data-driven predictors unreliable in small-sample settings. To address this issue, we propose a generation–prediction–interpretation framework that combines generative augmentation with physics-informed forecasting. We first develop a TCN-TimeGAN model to synthesize high-fidelity deformation sequences and expand the training set. Recurrent modules in the generator and discriminator are replaced with causal TCN residual blocks, and a temporal self-attention layer is further stacked on top of the TCN backbone to adaptively reweight informative time steps. We then construct a physics-informed Kolmogorov–Arnold Network, termed PI-KAN. Subsidence-consistency and smoothness priors are embedded in the learning objective to promote physically plausible predictions while retaining spline-based interpretability. Experiments on SBAS-InSAR deformation series from the Guqiao coal mine show that the framework achieves an RMSE of 0.825 mm and an R2 of 0.968. It outperforms TGAN-KAN, CNN-BiGRU, and BiGRU under the same evaluation protocol. Visualizations of the learned spline-based edge functions further reveal stronger nonlinear responses for lagged inputs closer to the forecast horizon, providing interpretable evidence of short-term temporal sensitivity under sparse observations.