In many real-world settings, image observations of freely rotating 3D rigid
bodies, 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. The usefulness of standard deep learning
methods is also limited because an image of a rigid body reveals nothing about
the distribution of mass inside the body, which, together with initial angular
velocity, is what determines how the body will rotate. 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. We demonstrate
the efficacy of our approach on new rotating rigid-body datasets of sequences
of synthetic images of rotating objects, including cubes, prisms and
satellites, with unknown uniform and non-uniform mass distributions.

使用多级预测管道，通过图像序列估计和预测三维旋转动力学，采用物理信息神经网络模型，并在旋转对象的合成图像序列数据集上展示了其有效性，包括正方体、棱柱和卫星等物体的未知均匀和非均匀质量分布。