Previous work on learning physical systems from data has focused on
high-resolution grid-structured measurements. However, real-world knowledge of
such systems (e.g. weather data) relies on sparsely scattered measuring
stations. In this paper, we introduce a novel simulated benchmark dataset,
DynaBench, for learning dynamical systems directly from sparsely scattered data
without prior knowledge of the equations. The dataset focuses on predicting the
evolution of a dynamical system from low-resolution, unstructured measurements.
We simulate six different partial differential equations covering a variety of
physical systems commonly used in the literature and evaluate several machine
learning models, including traditional graph neural networks and point cloud
processing models, with the task of predicting the evolution of the system. The
proposed benchmark dataset is expected to advance the state of art as an
out-of-the-box easy-to-use tool for evaluating models in a setting where only
unstructured low-resolution observations are available. The benchmark is
available at this https URL

本文介绍了一个新的模拟基准数据集 DynaBench, 用于直接从稀疏散乱的数据中学习动力系统。该数据集着重于通过低分辨率、非结构化的测量预测动力学系统的演变，并评估了几个机器学习模型（包括传统的图神经网络和点云处理模型）。