Learning Physics Informed Neural ODEs with Partial Measurements.

Area of Science:

• Control Systems Engineering
• Machine Learning
• Dynamical Systems Theory

Background:

• Learning dynamics in physical systems is difficult, particularly with partial state measurements.
• Unknown dynamics in unmeasured states pose a significant challenge for system identification.

Purpose of the Study:

• To develop a novel sequential optimization framework for learning system dynamics with unmeasured states.
• To address scenarios where the dynamics of unmeasured states are unknown.

Main Methods:

• Inspired by state estimation theory and Physics Informed Neural Ordinary Differential Equations (PINODEs).
• A sequential optimization framework is proposed to learn dynamics governing unmeasured processes.
• The approach integrates learning of unknown dynamics within a broader system identification context.

Main Results:

• The proposed framework successfully learns dynamics for systems with unmeasured states.
• Demonstrated performance using numerical simulations and a real-world electro-mechanical positioning system dataset.
• The method shows improved performance compared to baseline approaches in learning system dynamics.

Conclusions:

• The developed sequential optimization framework is effective for learning dynamics in partially observed systems.
• The approach provides a viable solution for identifying system dynamics when some states and their governing equations are unknown.
• This work advances the field of system identification for complex physical processes.