Learning dynamical systems is a promising avenue for scientific discoveries. However, capturing the governing dynamics in multiple environments still remains a challenge: model-based approaches rely on the fidelity of assumptions made for a single environment, whereas data-driven approaches based on neural networks are often fragile on extrapolating into the future. In this work, we develop a method of sparse regression dubbed SpReME to discover the major dynamics that underlie multiple environments. Specifically, SpReME shares a sparse structure of ordinary differential equation (ODE) across different environments in common while allowing each environment to keep the coefficients of ODE terms independently. We demonstrate that the proposed model captures the correct dynamics from multiple environments over four different dynamic systems with improved prediction performance.

翻译：学习动态系统是科学发现的一个有前景的途径。然而，在多个环境中捕捉主导动力学仍然是一个挑战：基于模型的方法依赖于针对单一环境所做假设的准确性，而基于神经网络的数据驱动方法往往在未来外推时表现脆弱。在本工作中，我们提出了一种名为SpReME的稀疏回归方法，以发现多个环境背后的主要动力学特性。具体而言，SpReME在不同环境之间共享一个稀疏结构的常微分方程（ODE），同时允许每个环境独立保留该ODE项的系数。我们证明了所提出的模型能够在四个不同动态系统上从多个环境中准确捕捉动力学特性，并具有更优的预测性能。