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

Abstract

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 the 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.

Unravelled multilevel transformation networks for predicting sparsely observed spatio-temporal dynamics

“…The forward network is a recurrent graph neural network with two recurrent GN blocks involving 2-layer GRU cells. We use the original model configuration mentioned in [22].…”

“…The same training settings are used for the DRC baseline, whereas for PADGN, we use the training settings of [22].…”

“…Some recent works address the problem of learning spatio-temporal dynamics from scattered data using graph networks (GNs) [19–22]. Belbute-Peres et al [19] augmented a low-resolution CFD solver with GN to learn a high-resolution solution.…”

“…Seo & Liu [21] proposed a differentiable physics-informed graph network (DPGN) incorporating data-specific physical equations into GNs. A more generic spatial difference layer on GN is proposed in [22], which can learn unknown spatio-temporal dynamics.…”

Meta-Learning Dynamics Forecasting Using Task Inference

“…The aim of meta learning, or learning to learn (Thrun & Pratt, 1998), is to acquire generic knowledge of different tasks in order for rapid learning on new tasks. Based on how the meta-level knowledge is extracted and used, meta-learning methods have been classified into model-based (Munkhdalai & Yu, 2017;Duan et al, 2017;Santoro et al, 2016;Alet et al, 2018;Oreshkin et al, 2019;Seo et al, 2020), metric-based (Vinyals et al, 2016;Snell et al, 2017) and gradient-based (Finn et al, 2017;Andrychowicz et al, 2016;Rusu et al, 2019;Grant et al, 2018;Yao et al, 2019). Most meta-learning approaches are outside of the forecasting domain with a few exceptions.…”