  Simulating physical systems is a core component of scientific computing,
encompassing a wide range of physical domains and applications. Recently, there
has been a surge in data-driven methods to complement traditional numerical
simulations methods, motivated by the opportunity to reduce computational costs
and/or learn new physical models leveraging access to large collections of
data. However, the diversity of problem settings and applications has led to a
plethora of approaches, each one evaluated on a different setup and with
different evaluation metrics. We introduce a set of benchmark problems to take
a step towards unified benchmarks and evaluation protocols. We propose four
representative physical systems, as well as a collection of both widely used
classical time integrators and representative data-driven methods
(kernel-based, MLP, CNN, nearest neighbors). Our framework allows evaluating
objectively and systematically the stability, accuracy, and computational
efficiency of data-driven methods. Additionally, it is configurable to permit
adjustments for accommodating other learning tasks and for establishing a
foundation for future developments in machine learning for scientific
computing.
