Symbolic pregression: Discovering physical laws from distorted video

Area of Science:

• Physics
• Machine Learning
• Computer Vision

Background:

• Discovering physical laws from observational data is a fundamental challenge.
• Traditional methods often require labeled data or controlled experiments.

Purpose of the Study:

• To develop an unsupervised method for learning equations of motion from unlabeled video data.
• To model predictable features in time-series data, even under distortions.

Main Methods:

• Training an autoencoder to map video frames to a low-dimensional latent space minimizing nonlinearity, acceleration, and prediction error.
• Employing Pareto-optimal symbolic regression to discover differential equations from the latent space representations.
• Utilizing a 'pregression' step involving added latent dimensions and principal component analysis for improved robustness.

Main Results:

• Successfully rediscovered Cartesian coordinates of unlabeled moving objects from raw and distorted synthetic videos.
• Demonstrated robustness to generalized lens distortions.
• Autodiscovered an inertial frame by minimizing combined equation complexity across multiple experiments.

Conclusions:

• The proposed unsupervised learning framework effectively discovers underlying physical laws of motion.
• The 'pregression' technique enhances the ability to model complex dynamics and handle data imperfections.
• This approach offers a powerful tool for scientific discovery from observational time-series data.