Automated Discovery of Operable Dynamics from Videos

TL;DR

This paper presents a novel framework that automatically discovers low-dimensional, operable representations of dynamical systems directly from videos, enabling scientific analysis without prior domain knowledge.

Contribution

It introduces a method to learn compact state variables and differentiable vector fields from videos, advancing automated discovery of system dynamics.

Findings

Successfully identified stable equilibria and natural frequencies.

Detected chaotic and limit cycle behaviors.

Demonstrated effectiveness across various dynamical systems.

Abstract

Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics, including a set of compact state variables that preserve the smoothness of the system dynamics and a differentiable vector field, directly from video without requiring prior domain-specific knowledge. The prominence and effectiveness of the proposed approach are demonstrated through both quantitative and qualitative analyses of a range of dynamical systems, including the identification of stable equilibria, the prediction of natural frequencies, and the detection of of chaotic and limit cycle behaviors. The results highlight the potential of our data-driven approach to advance automated scientific discovery.