Physics-informed epidemic prediction for irregularly sampled spatio-temporal sequence with missing values

In the task of predicting the spatiotemporal spread of the epidemic, a deep learning framework based on the discrete physics-informed neural network has been proposed, which integrates spatio-temporal dependency relationships and physical constraint mechanisms to address the limitations of traditional physics-informed neural networks. However, these methods typically assume that the spatiotemporal sequence is normally sampled at regular intervals and there are no missing values, without modeling the asynchronous spatiotemporal correlation present in irregularly sampled multivariate spatio-temporal sequences with missing values. The presence of missing values and variable time intervals in node variables in different regions may blur or distort the actual relationships between variables, which in turn affects the quality of loss-constrained learning of unknown parameters based on physical models. Therefore, this paper proposes a novel method for physics-informed spatiotemporal sequence prediction, named PEPIST. It utilizes a designed spatio-temporal sparse graph structure to effectively represent the irregularity of sampling time intervals and spatiotemporal missing values, and combines mechanisms such as graph spatiotemporal pattern capture and attention based physical spatiotemporal parameter interpolation to generate unknown parameter variable representations required for multi-region SEIR-informed loss constraints, as well as spatiotemporal characteristics of the variables to be predicted. Experimental results have shown that the method proposed in this paper exhibits high prediction accuracy in real COVID-19 epidemic prediction cases.