Deep kernel learning of dynamical models from high-dimensional noisy data.

Area of Science:

• Dynamical systems modeling
• Machine learning
• Data-driven discovery

Background:

• High-dimensional data often obscures underlying system dynamics.
• Traditional methods struggle with noise and dimensionality.
• Unsupervised learning offers a path to model discovery without labeled data.

Purpose of the Study:

• To develop a stochastic variational deep kernel learning method for identifying low-dimensional dynamical models.
• To enable data-driven discovery from high-dimensional, noisy measurements.
• To achieve unsupervised learning of system dynamics.

Main Methods:

• Utilizing an encoder to compress high-dimensional data into low-dimensional state variables.
• Implementing a latent dynamical model to predict system evolution.
• Employing a stochastic variational deep kernel learning framework for unsupervised training.

Main Results:

• Successfully denoised high-dimensional noisy RGB image measurements of a pendulum's motion.
• Learned compact state representations and accurate latent dynamical models.
• Effectively identified and quantified uncertainties in the learned dynamical models.

Conclusions:

• The proposed method enables robust discovery of dynamical models from complex data.
• It offers effective dimensionality reduction, denoising, and uncertainty quantification.
• This approach advances data-driven modeling for systems with continuous states and control inputs.