Recent approaches for modelling dynamics of physical systems with neural networks enforce Lagrangian or Hamiltonian structure to improve prediction and generalization. However, when coordinates are embedded in high-dimensional data such as images, these approaches either lose interpretability or can only be applied to one particular example. We introduce a new unsupervised neural network model that learns Lagrangian dynamics from images, with interpretability that benefits prediction and control. The model infers Lagrangian dynamics on generalized coordinates that are simultaneously learned with a coordinate-aware variational autoencoder (VAE). The VAE is designed to account for the geometry of physical systems composed of multiple rigid bodies in the plane. By inferring interpretable Lagrangian dynamics, the model learns physical system properties, such as kinetic and potential energy, which enables long-term prediction of dynamics in the image space and synthesis of energy-based controllers.
翻译:利用神经网络实施拉格朗吉亚或汉密尔顿结构的物理系统模拟动态的近期方法改进了预测和概括性。然而,当坐标嵌入图像等高维数据时,这些方法要么失去可解释性,要么只能适用于一个特定的例子。我们引入了一个新的不受监督的神经网络模型,从图像中学习拉格朗吉亚动态,其解释性有利于预测和控制。模型将拉格朗吉亚动态用于与协调意识自动变异器(VAE)同时学习的通用坐标上。VAE设计用于核算由飞机上多个僵硬体组成的物理系统的几何性。通过推断可解释的拉格朗吉亚动态,模型学习物理系统特性,例如动能和潜在能量,从而能够对图像空间中的动态进行长期预测,并合成以能源为基础的控制器。