论文标题
象征性预性：从扭曲的视频中发现物理定律
Symbolic Pregression: Discovering Physical Laws from Distorted Video
论文作者
论文摘要
我们提出了一种无监督学习的方法，以原始和未标记的视频中的对象方程式学习。我们首先训练一个自动编码器，该自动编码器将每个视频框架映射到一个低维的潜在空间中，在该空间中，运动定律尽可能简单，通过最大程度地减少非线性，加速度和预测错误的结合。然后，使用帕累托最佳符号回归发现描述运动的微分方程。我们发现，即使视频被广义镜头扭曲，我们的预回归（“预性”）步骤也能够重新发现未标记的移动对象的笛卡尔坐标。使用多维结理论的直觉，我们发现，首先添加额外的潜在空间维度来促进预性步骤，以避免在训练过程中避免拓扑问题，然后通过主成分分析去除这些额外的维度。
We present a method for unsupervised learning of equations of motion for objects in raw and optionally distorted unlabeled video. 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 non-linearity, 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.
