We introduce DeepBench, a Python library that employs mechanistic models (i.e., analytic mathematical models) to simulate data that represent physics-related objects and systems: geometric shapes (e.g., polygon), physics objects (e.g., pendulum), and astronomical objects (e.g., elliptical galaxy). These data take the form of images (two-dimensional) or time series (one-dimensional). In contrast to natural image benchmarks and complex physics simulations, these data have simple, direct, numerical, and traceable connections between the input data and the label data. When seeking a quantifiable interpretation, this kind of data is uniquely suitable for developing, calibrating, testing, and benchmarking statistical and machine learning models. Finally, this software package includes methods to curate and store these datasets to maximize reproducibility.