  We present a framework designed to learn the underlying dynamics between two
images observed at consecutive time steps. The complex nature of image data and
the lack of temporal information pose significant challenges in capturing the
unique evolving patterns. Our proposed method focuses on estimating the
intermediary stages of image evolution, allowing for interpretability through
latent dynamics while preserving spatial correlations with the image. By
incorporating a latent variable that follows a physical model expressed in
partial differential equations (PDEs), our approach ensures the
interpretability of the learned model and provides insight into corresponding
image dynamics. We demonstrate the robustness and effectiveness of our learning
framework through a series of numerical tests using geoscientific imagery data.
