论文标题
使用最佳运输和流形学习发现保护法
Discovering Conservation Laws using Optimal Transport and Manifold Learning
论文作者
论文摘要
保护定律是理解，表征和建模非线性动力学系统的关键理论和实用工具。但是，对于许多复杂的系统，相应的保守数量很难识别，因此很难分析其动态并构建稳定的预测模型。当前发现保护定律的方法通常取决于详细的动态信息或依赖黑匣子参数深度学习方法。相反，我们将这项任务重新制定为一种多种学习问题，并提出了一种发现保守数量的非参数方法。我们在各种物理系统上测试了这种新方法，并证明我们的方法能够识别保守数量的数量并提取其值。使用最佳传输理论和流形学习中的工具，我们提出的方法提供了一种直接的几何方法，用于识别既有坚固又可以解释的保护定律，而无需明确的系统模型或准确的时间信息。
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify, making it hard to analyze their dynamics and build stable predictive models. Current approaches for discovering conservation laws often depend on detailed dynamical information or rely on black box parametric deep learning methods. We instead reformulate this task as a manifold learning problem and propose a non-parametric approach for discovering conserved quantities. We test this new approach on a variety of physical systems and demonstrate that our method is able to both identify the number of conserved quantities and extract their values. Using tools from optimal transport theory and manifold learning, our proposed method provides a direct geometric approach to identifying conservation laws that is both robust and interpretable without requiring an explicit model of the system nor accurate time information.
