  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 (PDE) of data can be
helpful for the fast adaptation to few observations, it is mostly infeasible to
exactly find the equation for observations in real-world physical systems. In
this work, we propose a framework, physics-aware meta-learning with auxiliary
tasks, whose spatial modules incorporate PDE-independent knowledge and temporal
modules utilize the generalized features from the spatial modules to be adapted
to the limited data, respectively. The framework is inspired by a local
conservation law expressed mathematically as a continuity equation and does not
require the exact form of governing equation to model the spatiotemporal
observations. The proposed method mitigates the need for a large number of
real-world tasks for meta-learning by leveraging spatial information in
simulated data to meta-initialize the spatial modules. We apply the proposed
framework to both synthetic and real-world spatiotemporal prediction tasks and
demonstrate its superior performance with limited observations.
