论文标题
从自由旋转的3D刚体的图像中学习可解释的动态
Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Body
论文作者
论文摘要
在许多实际环境中，当低维测量值不足时，可能会提供自由旋转3D刚体（例如卫星）的图像观察。但是，图像数据的高维度排除了学习动力学和缺乏解释性的使用，从而降低了标准深度学习方法的有用性。在这项工作中，我们提出了一个物理信息的神经网络模型，以估计和预测图像序列中的3D旋转动力学。我们使用多阶段预测管道实现了这一目标，该管道将单个图像映射到潜在表示同构为$ \ Mathbf {so}（3）$，从潜在对计算角速度，并使用汉密尔顿的运动方程来预测未来的潜在状态，并具有汉密尔顿学会的动态。我们证明了方法对新的旋转刚体数据集的功效，该数据集具有旋转立方体和矩形棱镜的序列，其密度均匀且不均匀。
In many real-world settings, image observations of freely rotating 3D rigid bodies, such as satellites, may be available when low-dimensional measurements are not. However, the high-dimensionality of image data precludes the use of classical estimation techniques to learn the dynamics and a lack of interpretability reduces the usefulness of standard deep learning methods. In this work, we present a physics-informed neural network model to estimate and predict 3D rotational dynamics from image sequences. We achieve this using a multi-stage prediction pipeline that maps individual images to a latent representation homeomorphic to $\mathbf{SO}(3)$, computes angular velocities from latent pairs, and predicts future latent states using the Hamiltonian equations of motion with a learned representation of the Hamiltonian. We demonstrate the efficacy of our approach on a new rotating rigid-body dataset with sequences of rotating cubes and rectangular prisms with uniform and non-uniform density.
