论文标题
AIPoincaré2.0：机器学习保护法来自微分方程
AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations
论文作者
论文摘要
我们提出了一种机器学习算法，该算法从微分方程中发现保护定律，无论是在数字上（被参数为神经网络）还是象征性地，确保其功能独立性（对线性独立性的非线性概括）。我们的独立模块可以看作是单数值分解的非线性概括。我们的方法可以轻松地处理归纳偏见以进行保护法。我们用示例进行验证，包括3体问题，KDV方程和非线性Schrödinger方程。
We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schrödinger equation.
