论文标题
预测汉密尔顿动力学没有规范坐标
Forecasting Hamiltonian dynamics without canonical coordinates
论文作者
论文摘要
常规的神经网络是通用函数近似器，但是由于它们不知道潜在的对称性或物理定律，因此它们可能不切实际地需要许多训练数据才能近似于非线性动力学。最近引入的汉密尔顿神经网络可以有效地学习和预测节约能量的动力学系统，但它们需要特殊的输入，称为规范坐标，这可能很难从数据中推断出来。在这里，我们通过演示一种简单的方法来用任何一套广义坐标（包括易于观察的坐标）来训练它们，从而大大扩大了此类网络的范围。
Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here we significantly expand the scope of such networks by demonstrating a simple way to train them with any set of generalised coordinates, including easily observable ones.
