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math.NA2026
Fast Quadratic Manifold Learning For Nonlinear Dimensionality Reduction in Large-scale Systems using Riemannian Optimization
Gavin Paxton, Seunghee Cheon, Rudy Geelen +1
The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches ty…
math.NA2026★ 1 cited
A Dynamic Subspace Approach for Low-rank Approximation of Large-scale Nonlinear Systems
Jack DeChant, Rudy Geelen, Shane A. McQuarrie +1
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a…