Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey intrinsic physics, and struggle to cope with the various domains. While geometry-based methods, e.g., graph neural networks (GNNs), have been proposed to further tackle these challenges, they still need to find the implicit physical laws from large datasets and rely excessively on rich labeled data. In this paper, we herein introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework, to learn spatiotemporal dynamics based on limited training data. The network is designed to conform to the general conservation law via symmetry, where conservative and non-conservative information passes over a multiscale space enhanced by a latent temporal marching strategy. The efficacy of our model has been verified in various spatiotemporal systems based on synthetic and real-world datasets, showing superiority over baseline models. Results demonstrate that CiGNN exhibits remarkable accuracy and generalizability, and is readily applicable to learning for prediction of various spatiotemporal dynamics in a spatial domain with complex geometry.

本研究解决了在有限训练数据下，深度学习模型在时空动态预测中的不可解释性和物理规律缺失的问题。提出了一种名为保护信息图神经网络（CiGNN）的新方法，能够通过对称性遵循一般的守恒定律。研究表明，CiGNN在多个时空系统中表现出卓越的准确性和泛化能力，对复杂几何形态的时空动态预测具有显著潜力。

基于保护信息的图学习用于时空动态预测