Imaging Hyporheic Exchange by Integrating Deep Learning and Physics‐Informed Inversion of Time‐Lapse Self‐Potential Data

Abstract Self‐potential (SP) monitoring is increasingly used for subsurface flow characterization due to its sensitivity to hydrogeological and geochemical processes. However, SP inversion remains challenging due to its ill‐posed nature, sparse data coverage, and strong transient noise. This study proposes a hybrid framework to image hyporheic exchange using a time‐lapse SP data set monitored from a streamflow site in Oak Ridge, Tennessee. Dipole moment tomography grids generated from the physics‐informed numerical inversion is first used to train a Vision Transformer (ViT) model that maps surface SP sequences to 2D source distributions. While the numerical method is more responsive to transient signals, the ViT model better captures persistent spatial structures. Their complementary outputs are jointly analyzed in the spatiotemporal domain to isolate dynamic hyporheic exchange zones and distinguish transient from steady state subsurface flow features. This approach integrates physical inversion and deep learning to enhance interpretability, generalization, and temporal awareness in SP analysis.