Active Subspaces in Infinite Dimension

Poorbita Kundu, Nathan Wycoff

TL;DR: Supervised, linear dimension reduction using functional derivatives.

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 as well as improve modeling and optimization on complex test problems.

Submission Number: 918