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

Tomoki Koike; Benjamin Peherstorfer; Elizabeth Qian

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arXiv · 2610.33784

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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Tomoki Koike, Benjamin Peherstorfer, Elizabeth Qian. 2026-10-24. Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling. https://arxiv.org/abs/2610.33784

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