Robust Low-Rank Tensor Approximation of Koopman Operators from Incomplete and Contaminated Lifted Data

Source abstract

Tensor-product dictionaries improve the expressiveness of finite-dimensional Koopman models but produce exponentially large dense operators, while least-squares fitting is sensitive to incomplete and contaminated data. We propose a robust tensor Koopman operator (RTKO) estimator for fully observed current states and partially observed or corrupted lifted outputs. RTKO combines a canonical polyadic (CP) operator with an observation mask and a sparse error variable; eliminating the error yields a Huber loss on observed residuals. A proximal alternating algorithm updates the error by soft thresholding and the factors by masked ridge regression. Under stated Kurdyka–Łojasiewicz assumptions, the iterates converge to a critical point. On the Lorenz benchmark, RTKO reduces one-step RMSE relative to non robust CP regression by 87.9% under entrywise corruption and by 94.4% under whole sample corruption. On controlled orbit transfer, the corresponding reduction is 57.9%, and RTKO-based MPC succeeds in 9 of 10 contaminated data fits versus 0 of 10 for the non robust CP model. Dense robust EDMD remains more accurate on these low dimensional systems, whereas RTKO reduces operator storage.