Recent studies to learn physical laws via deep learning attempt to find the
shared representation of the given system by introducing physics priors or
inductive biases to the neural network. However, most of these approaches
tackle the problem in a system-specific manner, in which one neural network
trained to one particular physical system cannot be easily adapted to another
system governed by a different physical law. In this work, we use a
meta-learning algorithm to identify the general manifold in neural networks
that represents Hamilton's equation. We meta-trained the model with the dataset
composed of five dynamical systems each governed by different physical laws. We
show that with only a few gradient steps, the meta-trained model adapts well to
the physical system which was unseen during the meta-training phase. Our
results suggest that the meta-trained model can craft the representation of
Hamilton's equation in neural networks which is shared across various dynamical
systems with each governed by different physical laws.

通过元学习算法，本研究使用包含五种不同物理定律的数据集来识别神经网络中代表哈密顿方程的一般流形，并表明元训练模型可以在元训练阶段未见过的物理系统上适应，其能够在各种不同的动力系统中共享哈密顿方程的神经网络表示。