Learning Discrepancy Models From Experimental Data
This work addresses the challenge of model inaccuracies in complex physical systems, such as mechanical systems with nonlinear friction, which is incremental as it applies an existing method to a specific domain.
The paper tackles the problem of modeling discrepancies between simplified physical models and experimental data in nonlinear systems, using the SINDy algorithm to discover sparse discrepancy models and demonstrating efficacy on examples like a double pendulum on a cart, with simulations showing improved feed-forward control.
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.