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.
翻译:最近通过深层学习来学习物理法的研究,试图通过引入物理前科或对神经网络的感性偏差,找到特定系统的共同代表性。然而,大多数这些方法都以系统特定的方式解决问题,即一个受过特定物理系统训练的神经网络无法轻易地适应由不同物理法管理的另一个系统。在这项工作中,我们使用元学习算法来识别神经网络中代表汉密尔顿方程式的一般多元体。我们用由五个动态系统组成的数据集对模型进行元培训,每个系统由五个动态系统组成,由不同的物理法管理。我们显示,只有几个梯度步骤,元培训模型就能很好地适应元培训阶段所看不到的物理系统。我们的结果表明,经过元培训的模型可以在神经网络中构建汉密尔顿方程式的方程式,而神经网络由不同的动态系统共同组成,每个系统都受不同的物理法管辖。