State estimation of a physical system with unknown governing equations

Area of Science:

• Machine Learning
• Control Theory
• Applied Mathematics

Background:

• State estimation reconciles noisy observations with system models to infer unmeasurable states.
• Traditional methods assume specific uncertainty forms (e.g., additive stochastic or parametric).
• Many real-world systems have partially or fully unknown dynamics, limiting classical approaches.

Purpose of the Study:

• To develop an approximate Bayesian state estimation method for systems with unknown dynamics.
• To enable simultaneous learning of unknown model terms and system states.
• To extend the applicability of state estimation to previously intractable problems.

Main Methods:

• A reparametrization trick for stochastic variational inference with Markov Gaussian processes.
• An approximate Bayesian framework for learning unknown system dynamics.
• Simultaneous estimation of system states and model parameters.

Main Results:

• The proposed method effectively performs state estimation with partially or completely unknown system evolution equations.
• It learns missing terms in the mathematical model and estimates states concurrently.
• Demonstrates a novel approach to handling model uncertainty in state estimation.

Conclusions:

• The developed technique advances approximate Bayesian inference for state estimation.
• It significantly broadens the scope of problems addressable by state estimation.
• The advancements in stochastic variational inference have broader implications for machine learning.