Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses the challenge of identifying such subspaces automatically: given as input an energy function for a high-dimensional system, we produce a low-dimensional map whose image parameterizes a diverse yet low-energy submanifold of configurations. The only additional input needed is a single seed configuration for the system to initialize our procedure; no dataset of trajectories is required. We represent subspaces as neural networks that map a low-dimensional latent vector to the full configuration space, and propose a training scheme to fit network parameters to any system of interest. This formulation is effective across a very general range of physical systems; our experiments demonstrate not only nonlinear and very low-dimensional elastic body and cloth subspaces, but also more general systems like colliding rigid bodies and linkages. We briefly explore applications built on this formulation, including manipulation, latent interpolation, and sampling.

翻译：从弹性体到运动链等物理系统均定义在高维构型空间上，但其典型低能构型高度集中于更低维的子空间。本研究旨在解决自动识别此类子空间的挑战：以高维系统的能量函数作为输入，我们生成一个低维映射，其像参数化一个多样但低能的构型子流形。所需额外输入仅为初始化过程的单一种子构型，无需轨迹数据集。我们将子空间表示为将低维潜变量映射至全构型空间的神经网络，并提出一种训练方案以适配任意目标系统的网络参数。该公式适用于极广泛的物理系统范围；实验不仅展示了非线性且极低维的弹性体与布料子空间，还涵盖更通用的系统如碰撞刚体与运动链。我们简要探索了基于该公式的应用，包括操控、潜变量插值与采样。