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.

翻译：我们提出了一种旨在学习连续时间步长下两幅观测图像间潜在动态过程的框架。图像数据的复杂性和时间信息的缺失对捕捉独特的演化模式构成了重大挑战。所提出的方法聚焦于估计图像演化的中间阶段，通过潜在动态实现可解释性，同时保持与图像的空间相关性。通过引入遵循偏微分方程所描述的物理模型的潜变量，我们的方法确保了学习模型的可解释性，并提供了对相应图像动态过程的洞察。我们利用地球科学图像数据开展了一系列数值测试，验证了学习框架的鲁棒性和有效性。