Mathematics· 2026Q2
Robust Low-Rank Tensor Approximation of Koopman Operators from Incomplete and Contaminated Lifted Data
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- Q2SCImago
- 2026year
Short summary
A new Robust Tensor Koopman Operator (RTKO) estimator significantly reduces errors in predicting system dynamics from incomplete or corrupted data, achieving up to 94.4% lower RMSE on benchmarks.
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Key points
- RTKO estimator handles incomplete or corrupted lifted data for Koopman operator approximation.
- Combines a canonical polyadic (CP) operator with an observation mask and sparse error variable, using Huber loss.
- Proximal alternating algorithm updates error via soft thresholding and factors via masked ridge regression.
- RTKO reduced one-step RMSE by up to 94.4% on the Lorenz benchmark and 57.9% on controlled orbit transfer with corrupted data.
- RTKO-based MPC succeeded in 9/10 contaminated data fits for orbit transfer, vs. 0/10 for non-robust CP.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. Mathematics, 2026 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics