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充满希望的渠道。然而,捕捉多种环境中的治理动态仍是一个挑战:基于模型的方法依赖于为单一环境所作的假设的忠实性,而基于神经网络的数据驱动方法往往在外推未来时很脆弱。在这项工作中,我们开发了一种被称为SpReME的稀疏回归方法,以发现多种环境背后的主要动态。具体地说,SpreME在不同环境中共享一种稀疏的普通差异方程式结构,在共同的环境中允许每个环境独立保持ODE术语的系数。我们证明,拟议的模型从四个不同的动态系统中从多种环境中捕捉了正确的动态,而预测性能则有所改善。</s>