Physics-aware Spatiotemporal Modules with Auxiliary Tasks for Meta-Learning

Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder directly applying meta-learning techniques. Although the knowledge of governing partial differential equations (PDEs) of the data can be helpful for the fast adaptation to few observations, it is difficult to generalize to different or unknown dynamics. In this paper, we propose a framework, physics-aware modular meta-learning with auxiliary tasks (PiMetaL) whose spatial modules incorporate PDE-independent knowledge and temporal modules are rapidly adaptable to the limited data, respectively. The framework does not require the exact form of governing equations to model the observed spatiotemporal data. Furthermore, it mitigates the need for a large number of real-world tasks for meta-learning by leveraging simulated data. We apply the proposed framework to both synthetic and real-world spatiotemporal prediction tasks and demonstrate its superior performance with limited observations.