Active Subspaces in Infinite Dimension

Poorbita Kundu; Nathan Wycoff

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arXiv · 2510.11871

Active Subspaces in Infinite Dimension

Poorbita Kundu·Nathan Wycoff

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Abstract

Active subspace analysis uses the leading eigenspace of the gradient's second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations and improve modeling and optimization on complex test problems.

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BibTeX RIS

Poorbita Kundu, Nathan Wycoff. 2025-10-13. Active Subspaces in Infinite Dimension. https://arxiv.org/abs/2510.11871

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