Prediction of volcanic and earthquake-triggered deformation using Neural Deformation Field (NDF) modeling in Fentale, Ethiopia

This study investigates the prediction of volcanic and earthquake-triggered deformation at Mount Fentale using remote sensing (InSAR) and machine learning. Sentinel-1 SAR data from January 2024 to January 2026 were processed with a small-baseline InSAR (SB-InSAR) approach, integrating HyP3 and MintPy for data downloading, stacking, and time-series analysis. The work introduces a novel physics-informed deep learning framework—neural deformation field (NDF)—that addresses the limitations of traditional Extended Trajectory Models (ETMs) by learning spatially continuous deformation fields while preserving the physical interpretability of classical geodetic models. The NDF model was validated using ETM (temporal domain), Kriging (spatial domain), and standard MLP (non-physics-informed) models. The NDF efficiency was confirmed by mutual comparison with these alternative models. InSAR time series at the center of the Fentale crater capture surface deformation associated with a major dike intrusion and an earthquake sequence in early 2025. A long-term subsidence of −3.0 ± 2.2 cm/yr was abruptly interrupted on January 10, 2025, by a co-seismic step of −35.5 ± 1.8 cm, coinciding with M 5.8 and M 5.7 earthquakes. After the event, the post-intrusion velocity accelerated to −4.8 ± 3.8 cm/yr. A neural deformation field trained after removing the major earthquake event predicts a cumulative uplift of ~6–8 cm at the crater over 2025–2026. The neural model achieves an overall root mean square error of 1.9 cm across the study area, demonstrating robust performance for most spatial locations. These results highlight the need for nonlinear transient terms to capture near-field post-seismic rebound at volcanic craters. The steady transition from a stable state to this high-magnitude, localized uplift suggests a consistent and focused magmatic flux into a shallow reservoir or dike system following the seismic event.