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.
翻译:模拟现实世界物理系统的动态对于时空预测任务至关重要,但当数据有限时则具有挑战性。现实世界数据稀缺,数据分配难于再生,这妨碍了直接应用元学习技术。虽然管理数据部分差异方程式(PDE)的知识有助于快速适应少数观测,但大部分无法准确找到在现实世界物理系统中观测的方程式。在这项工作中,我们提出了一个框架,即以辅助任务进行物理认知元学习,其空间模块包含PDE依赖性知识和时间模块,利用空间模块的普遍特征分别适应有限的数据。该框架受一个数学表达为连续性方程式的地方保护法的启发,不需要精确的治理方程式来模拟空间时空观测。拟议方法通过利用模拟数据中的空间信息来使空间模块形成元化,减轻大量实际世界的元学习任务的必要性。我们将拟议框架应用于合成和现实世界空间模块,并展示其高超水平的观测任务。