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Found 8 papers, 3 papers with code
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.
Quadrupole Magnet Design based on Genetic Multi-Objective Optimization
This work suggests to optimize the geometry of a quadrupole magnet by means of a genetic algorithm adapted to solve multi-objective optimization problems.
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.
Grassmannian diffusion maps based surrogate modeling via geometric harmonics
Using this representation, geometric harmonics, an out-of-sample function extension technique, is employed to create a global map from the space of input parameters to a Grassmannian diffusion manifold.
Manifold learning-based polynomial chaos expansions for high-dimensional surrogate models
For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner.
Robust Adaptive Least Squares Polynomial Chaos Expansions in High-Frequency Applications
We present an algorithm for computing sparse, least squares-based polynomial chaos expansions, incorporating both adaptive polynomial bases and sequential experimental designs.
Computational Engineering, Finance, and Science
Uncertainty quantification for an optical grating coupler with an adjoint-based Leja adaptive collocation method
By combining the Leja adaptive algorithm with an adjoint-based error indicator, an even smaller complexity is obtained.
Computational Engineering, Finance, and Science Numerical Analysis Computational Physics Optics 60H15, 60H35, 65N30, 78A40, 78M10 I.6.3; J.2; G.1.8
Assessing the Performance of Leja and Clenshaw-Curtis Collocation for Computational Electromagnetics with Random Input Data
We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters.
Computational Engineering, Finance, and Science Numerical Analysis Numerical Analysis Computation 78Axx, 65D30, 65D32, 65D15, 65D05, 68U20, 65C20
