Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909039646998528 |
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| author | Shah, Dhruv Cortés, Jorge |
| author_facet | Shah, Dhruv Cortés, Jorge |
| contents | The accuracy of Koopman operator approximations over
finite-dimensional spaces relies critically on their invariance
properties. These can be rigorously quantified via the principal
angles between a candidate subspace and its image under the Koopman
operator. This paper proposes a unified algebraic framework for
subspace pruning designed to systematically refine the invariance
error. We establish the geometric equivalence between
consistency-based methods and principal-vector pruning, and build on
this insight to introduce a hybrid strategy that balances between
multiple and single principal vector pruning for improved numerical
stability and scalability. We derive error bounds for the retention
of approximate and external eigenfunctions, demonstrating that the
multi-vector approach mitigates the numerical drift inherent to
sequential pruning. To ensure scalability, we develop an efficient
numerical update scheme based on rank-one modifications that reduces
the computational complexity of tracking principal angles by an
order of magnitude. Finally, we exploit the subspace obtained from
the pruning algorithms to build a lifted linear model for state
prediction that accounts for the trade-offs between improving
invariance and minimizing state reconstruction error. Simulations
demonstrate the effectiveness of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13135 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations Shah, Dhruv Cortés, Jorge Systems and Control The accuracy of Koopman operator approximations over finite-dimensional spaces relies critically on their invariance properties. These can be rigorously quantified via the principal angles between a candidate subspace and its image under the Koopman operator. This paper proposes a unified algebraic framework for subspace pruning designed to systematically refine the invariance error. We establish the geometric equivalence between consistency-based methods and principal-vector pruning, and build on this insight to introduce a hybrid strategy that balances between multiple and single principal vector pruning for improved numerical stability and scalability. We derive error bounds for the retention of approximate and external eigenfunctions, demonstrating that the multi-vector approach mitigates the numerical drift inherent to sequential pruning. To ensure scalability, we develop an efficient numerical update scheme based on rank-one modifications that reduces the computational complexity of tracking principal angles by an order of magnitude. Finally, we exploit the subspace obtained from the pruning algorithms to build a lifted linear model for state prediction that accounts for the trade-offs between improving invariance and minimizing state reconstruction error. Simulations demonstrate the effectiveness of our approach. |
| title | Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.13135 |