  First principles modeling of physical systems has led to significant
technological advances across all branches of science. For nonlinear systems,
however, small modeling errors can lead to significant deviations from the
true, measured behavior. Even in mechanical systems, where the equations are
assumed to be well-known, there are often model discrepancies corresponding to
nonlinear friction, wind resistance, etc. Discovering models for these
discrepancies remains an open challenge for many complex systems. In this work,
we use the sparse identification of nonlinear dynamics (SINDy) algorithm to
discover a model for the discrepancy between a simplified model and measurement
data. In particular, we assume that the model mismatch can be sparsely
represented in a library of candidate model terms. We demonstrate the efficacy
of our approach on several examples including experimental data from a double
pendulum on a cart. We further design and implement a feed-forward controller
in simulations, showing improvement with a discrepancy model.
