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.

我们提出了一个框架，旨在学习两个连续时间步骤中观察到的图像之间的基本动态。通过估计图像演化的中间阶段，我们的方法关注在保持图像的空间相关性的同时提供可解释性，并通过偏微分方程中表示的物理模型引入潜在动态学变量，确保了所学模型的可解释性并提供了相应图像动态的洞察力。通过对地球科学图像数据进行一系列数值测试，我们证明了我们学习框架的鲁棒性和有效性。