SpReME: Sparse Regression for Multi-Environment Dynamic Systems

MoonJeong Park, Youngbin Choi, Dongwoo Kim

Keywords: dynamics discovery, machine learning, incomplete prior, sparse regression, multi-environment

TL;DR: Sparse Regression for Multi-Environment Dynamic Systems

Abstract:

Learning dynamical systems provides a new opportunity to tackle a central challenge in science and engineering.
Model-based approaches show promising results with data samples captured from a single environment. On the other hand, pure data-driven approaches provide plausible results in extracting governing dynamics from multiple environments. The data-driven approach, however, raises a concern about the forecasting of dynamics as recent studies show the limitations of neural networks on extrapolation.
In this work, we propose sparse regression for multi-environment (SpReME) that can leverage the best of both model-based and data-driven approaches to extract the governing dynamics from multiple environments. We cast the dynamic discovery as a sparse regression problem over multiple environments. The bases of the regression model can be curated with incomplete prior knowledge.
We demonstrate our framework on four different dynamic systems ranging from simple linear to complex chaotic systems. The experimental results show that the extracted knowledge from multiple environments can be generalized to predict the dynamics of an unseen environment.