Symbolic Pregression: Discovering Physical Laws from Distorted Video

TL;DR

This paper introduces a method called Symbolic Pregression that learns physical laws from raw, possibly distorted videos by combining autoencoders and symbolic regression to discover simple equations of motion.

Contribution

It proposes a novel pre-regression step that effectively uncovers object coordinates even in distorted videos, enhancing physical law discovery from unlabeled data.

Findings

Successfully rediscovered object coordinates in distorted videos

Enhanced symbolic regression with a pre-regression step

Utilized multidimensional knot-theory for improved latent space handling

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.