UC Davis

Koopman Operator theory opens the door for application of rich linear systems theory to data-driven modeling and control of nonlinear dynamic systems. Fusing Gaussian Processes with Koopman models holds the promise of principled uncertainty quantification and improved representational flexibility. However, existing approaches fail to properly utilize the strengths of Gaussian Process Regression. Thus, we present inverted Gaussian Process optimization based probabilistic Koopman Operator learning (iGPK), an automatic differentiation-based approach to jointly learn the observable-operator combination. The proposed learning framework is shown to converge to stationary points under minimal assumptions. Our extensive numerical studies show that iGPK is robust to observation noise in the training data, while also providing good uncertainty quantification, such that the predicted distribution consistently encapsulates the ground truth.