Udrescu Silviu-Marian, Tegmark Max
Department of Physics, Institute for AI & Fundamental Interactions, and Center for Brains, Minds, & Machines, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E. 2021 Apr;103(4-1):043307. doi: 10.1103/PhysRevE.103.043307.
We present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled synthetic video (or, more generally, for discovering and modeling predictable features in time-series data). We first train an autoencoder that maps each video frame into a low-dimensional latent space where the laws of motion are as simple as possible, by minimizing a combination of nonlinearity, acceleration, and prediction error. Differential equations describing the motion are then discovered using Pareto-optimal symbolic regression. We find that our pre-regression ("pregression") step is able to rediscover Cartesian coordinates of unlabeled moving objects even when the video is distorted by a generalized lens. Using intuition from multidimensional knot theory, we find that the pregression step is facilitated by first adding extra latent space dimensions to avoid topological problems during training and then removing these extra dimensions via principal component analysis. An inertial frame is autodiscovered by minimizing the combined equation complexity for multiple experiments.
我们提出了一种用于对原始且可能失真的未标记合成视频中的物体运动方程进行无监督学习的方法（或者更一般地说，用于在时间序列数据中发现并建模可预测特征）。我们首先训练一个自动编码器，通过最小化非线性、加速度和预测误差的组合，将每个视频帧映射到一个低维潜在空间，在该空间中运动定律尽可能简单。然后使用帕累托最优符号回归来发现描述运动的微分方程。我们发现，即使视频因广义透镜而失真，我们的预回归（“pregression”）步骤也能够重新发现未标记移动物体的笛卡尔坐标。利用多维纽结理论的直觉，我们发现通过首先添加额外的潜在空间维度以避免训练期间的拓扑问题，然后通过主成分分析去除这些额外维度，预回归步骤会变得更容易。通过最小化多个实验的组合方程复杂度自动发现惯性系。
