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Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification
To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data.
A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems
Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional $\mathcal{O}(10^{\ge 2})$ stochastic inputs (e. g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges.
Data-driven Uncertainty Quantification in Computational Human Head Models
This framework is demonstrated on a 2D subject-specific head model, where the goal is to quantify uncertainty in the simulated strain fields (i. e., output), given variability in the material properties of different brain substructures (i. e., input).
