no code implementations • 23 Jul 2023 • Aimee Maurais, Terrence Alsup, Benjamin Peherstorfer, Youssef Marzouk
We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices.
1 code implementation • 31 Jan 2023 • Aimee Maurais, Terrence Alsup, Benjamin Peherstorfer, Youssef Marzouk
We introduce a multi-fidelity estimator of covariance matrices that employs the log-Euclidean geometry of the symmetric positive-definite manifold.
no code implementations • 6 Dec 2022 • Terrence Alsup, Tucker Hartland, Benjamin Peherstorfer, Noemi Petra
Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs and fidelity to computationally speed up inference.
no code implementations • 5 Apr 2021 • Terrence Alsup, Luca Venturi, Benjamin Peherstorfer
The proposed multilevel Stein variational gradient descent moves most of the iterations to lower, cheaper levels with the aim of requiring only a few iterations on the higher, more expensive levels when compared to the traditional, single-level Stein variational gradient descent variant that uses the highest-level distribution only.
no code implementations • 22 Oct 2020 • Terrence Alsup, Benjamin Peherstorfer
Thus, there is a trade-off between investing computational resources to improve the accuracy of surrogate models versus simply making more frequent recourse to expensive high-fidelity models; however, this trade-off is ignored by traditional modeling methods that construct surrogate models that are meant to replace high-fidelity models rather than being used together with high-fidelity models.