English

Symbolic Pregression: Discovering Physical Laws from Distorted Video

Computer Vision and Pattern Recognition 2021-04-28 v2 Artificial Intelligence Machine Learning Computational Physics Machine Learning

Abstract

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.

Keywords

Cite

@article{arxiv.2005.11212,
  title  = {Symbolic Pregression: Discovering Physical Laws from Distorted Video},
  author = {Silviu-Marian Udrescu and Max Tegmark},
  journal= {arXiv preprint arXiv:2005.11212},
  year   = {2021}
}

Comments

Expanded and improved physics discussion, additional method details. 9 pages, 7 figs

R2 v1 2026-06-23T15:44:31.907Z