DynaBench: A benchmark dataset for learning dynamical systems from low-resolution data

Abstract: This is the meta-repository for the DynaBench dataset - a benchmark dataset for learning physical systems from low-resolution, non-grid data. The benchmark contains simulations of several physical systems (advection, burgers', gas dynamics, kuramoto-sivashinsky, reaction-diffusion, wave). Each system has been simulated several times using a high-resolution numerical solver, from which the observations have been sampled at different resolutions (low, medium, high) as well as two different spatial structures (grid, scattered). TechnicalInfo: The dataset is split into 42 parts (6 equations x 7 combinations of resolution/structure). Each part can be downloaded separately and contains 7000 simulations of the given equation at the given resolution and structure. The simulations are grouped into chunks of 500 simulations saved in the hdf5 file format. Each chunk contains the variable "data", where the values of the simulated system are stored, as well as the variable "points", where the coordinates at which the system has been observed are stored. For more details visit the DynabBench website at https://professor-x.de/dynabench/. The dataset is best used as part of the dynabench python package available at https://pypi.org/project/dynabench/. Abstract: 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://professor-x.de/dynabench.