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.

本文提出一种物理知识指导的神经网络模型，能够从图像序列中估算预测旋转刚体的 3D 动力学，多阶段预测管道映射图像到与 SO (3) 同胚的潜在表示，通过学习得到的哈密顿表示，利用哈密顿运动方程预测未来的潜在状态。