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Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling

  • Tomoki Koike
  • Benjamin Peherstorfer
  • Elizabeth Qian
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Abstract

Polynomial manifolds provide nonlinear low-dimensional representations through polynomial decoders. We propose to represent the polynomial terms of the decoder using features that are orthonormal on the training data. This empirical orthogonality enables a greedy algorithm, Greedy-OPM, which jointly selects encoder modes and polynomial features while minimizing the reconstruction error under a prescribed bound on the decoder's Lipschitz constant. Numerical experiments show that this Lipschitz constraint improves generalization away from the training data while retaining high reconstruction accuracy.

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Cite

BibTeXRIS
BibTeX
@misc{koike2026greedy,
  title = {{Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling}},
  author = {Tomoki Koike and Benjamin Peherstorfer and Elizabeth Qian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33784},
  eprint = {2610.33784},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33784},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling
AU  - Tomoki Koike
AU  - Benjamin Peherstorfer
AU  - Elizabeth Qian
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33784
UR  - https://arxiv.org/abs/2610.33784
AB  - Polynomial manifolds provide nonlinear low-dimensional representations through polynomial decoders. We propose to represent the polynomial terms of the decoder using features that are orthonormal on the training data. This empirical orthogonality enables a greedy algorithm, Greedy-OPM, which jointly selects encoder modes and polynomial features while minimizing the reconstruction error under a prescribed bound on the decoder's Lipschitz constant. Numerical experiments show that this Lipschitz constraint improves generalization away from the training data while retaining high reconstruction accuracy.
ER  -