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 https://anonymous.4open.science/r/code-2022-dynabench/.

翻译：以往从数据中学习物理系统的工作主要聚焦于高分辨率网格结构化测量。然而，现实世界中此类系统（例如气象数据）的知识依赖于稀疏分布的测量站点。本文提出了一种新的模拟基准数据集DynaBench，用于直接从稀疏分布的数据中学习动力系统，无需事先了解方程。该数据集专注于从低分辨率、非结构化测量中预测动力系统的演化。我们模拟了六种不同的偏微分方程，涵盖文献中常用的多种物理系统，并评估了多种机器学习模型，包括传统图神经网络和点云处理模型，任务目标是预测系统的演化状态。所提出的基准数据集有望作为一种开箱即用、易于使用的工具，推动在仅有非结构化低分辨率观测数据的场景下评估模型的先进技术发展。该基准数据集可通过https://anonymous.4open.science/r/code-2022-dynabench/获取。