Stochastic collocation on unstructured multivariate meshes

Abstract

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction are becoming standard tools used in a variety of applications. Selection of a collocation mesh is frequently a challenge, but methods that construct geometrically "unstructured" collocation meshes have shown great potential due to attractive theoretical properties and direct, simple generation and implementation. We investigate properties of these meshes, presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.

29 pages, 6 figures

References in corpus (2)

• Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation
• Weighted Pluripotential Theory Results of Berman-Boucksom

Cited by in corpus (15)

• Polynomial approximation via compressed sensing of high-dimensional functions on lower sets
• A Christoffel function weighted least squares algorithm for collocation approximations
• Compressed sensing with sparse corruptions: Fault-tolerant sparse collocation approximations
• A gradient enhanced ${\ell }_1$-minimization for sparse approximation of polynomial chaos expansions
• Data-driven polynomial chaos expansions: a weighted least-square approximation
• An adaptive reduced basis ANOVA method for high-dimensional Bayesian inverse problems
• Approximating smooth, multivariate functions on irregular domains
• Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
• Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points
• Optimal sampling rates for approximating analytic functions from pointwise samples
• Infinite-dimensional compressed sensing and function interpolation
• Particle based gPC methods for mean-field models of swarming with uncertainty
• Stochastic collocation methods via $L_1$ minimization using randomized quadratures
• Near-optimal sampling strategies for multivariate function approximation on general domains
• Weighted approximate Fekete points: Sampling for least-squares polynomial approximation