6 papers
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…
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…
Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces
Alejandro N Diaz, Shane A McQuarrie, John T Tencer +1
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynam…
Active learning for data-driven reduced models of parametric differential systems with Bayesian operator inference
Shane A. McQuarrie, Mengwu Guo, Anirban Chaudhuri
This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation o…
Tensor parametric Hamiltonian operator inference
Arjun Vijaywargiya, Shane A. McQuarrie, Anthony Gruber
This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian st…
Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems
Shane A. McQuarrie, Anirban Chaudhuri, Karen E. Willcox +1
This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use…