论文标题
通过从受过训练的深层神经网络中得出动态的对称性来解释的保护法估计
Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networks
论文作者
论文摘要
了解复杂的系统及其减少模型是科学活动中的核心作用之一。尽管物理学家的物理见解大大发展了物理学，但仅仅基于见解，建立这种复杂系统的减少模型有时具有挑战性。我们提出了一个新颖的框架，可以从深层神经网络（DNN）中推断出已通过系统物理数据训练的复杂系统的隐藏保护定律。该框架的目的不是用深度学习分析物理数据，而是从训练有素的DNN中提取可解释的物理信息。使用Noether的定理和通过有效的抽样方法，提出的框架通过从训练有素的DNN中提取动力学对称性来渗透保护定律。提出的框架是通过得出时间序列数据集的多种关系结构与Noether定理的必要条件之间的关系而开发的。在某些原始案例中，已验证了拟议框架的可行性，而保护法是众所周知的。我们还将提出的框架应用于保护法的估计，以估算更实际的案例，该案例是一个大规模的集体运动系统，在亚稳态状态下，我们获得的结果与先前的研究相一致。
Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a reduced model of such complex systems on the basis of insights alone. We propose a novel framework that can infer the hidden conservation laws of a complex system from deep neural networks (DNNs) that have been trained with physical data of the system. The purpose of the proposed framework is not to analyze physical data with deep learning, but to extract interpretable physical information from trained DNNs. With Noether's theorem and by an efficient sampling method, the proposed framework infers conservation laws by extracting symmetries of dynamics from trained DNNs. The proposed framework is developed by deriving the relationship between a manifold structure of time-series dataset and the necessary conditions for Noether's theorem. The feasibility of the proposed framework has been verified in some primitive cases for which the conservation law is well known. We also apply the proposed framework to conservation law estimation for a more practical case that is a large-scale collective motion system in the metastable state, and we obtain a result consistent with that of a previous study.
