Physics-informed multi-output Gaussian process for dynamical system modeling.

Area of Science:

• Dynamical Systems Modeling
• Machine Learning
• Robotics
• Control Theory

Background:

• Accurate dynamics models are essential for model-based reinforcement learning.
• Standard Gaussian Processes (GPs) model system dimensions independently, missing inter-dependencies.
• Existing multi-output GPs capture correlations but often lack interpretability in dynamical systems.

Purpose of the Study:

• To propose a novel physics-informed multi-output Gaussian process (P-MO-GP) for enhanced dynamical system modeling.
• To improve the interpretability and accuracy of multi-output Gaussian processes by integrating physical knowledge.
• To demonstrate superior performance compared to existing methods in learning dynamics models and control tasks.

Main Methods:

• Incorporated a physics-informed prior using the Lagrangian method into a multi-output Gaussian process framework.
• Defined GP mean functions using a discretized physical model, sharing a common physical parameter across dimensions.
• Employed a fully Bayesian approach, treating all hyperparameters as random variables and utilizing a probabilistic graphical model.

Main Results:

• Proved that unknown physical parameters induce dependencies among all system dimensions.
• Demonstrated that P-MO-GP learns more accurate dynamics models than single-output and standard multi-output GPs.
• Achieved improved control performance and greater robustness to observation noise compared to baseline methods.

Conclusions:

• Physics-informed multi-output Gaussian processes offer an interpretable and principled method for correlating dynamical system dimensions.
• P-MO-GP effectively leverages physical knowledge to enhance learning accuracy and control capabilities.
• The proposed model shows significant advantages in complex dynamical system modeling and reinforcement learning applications.