Stochastic Collocation with Non-Gaussian Correlated Parameters via a New Quadrature Rule

TL;DR

This paper introduces a new quadrature rule for stochastic collocation methods that efficiently handles correlated non-Gaussian parameters, enabling faster uncertainty quantification in complex systems.

Contribution

It proposes an optimization-based quadrature rule and solver for multivariate integration with correlated non-Gaussian parameters, extending stochastic collocation capabilities.

Findings

Achieved 3000x speedup over Monte Carlo methods

Validated on CMOS ring oscillator and optical ring resonator

Effectively handles correlated non-Gaussian uncertainties

Abstract

This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient of each basis function via a projection step. We propose an optimization model and a block coordinate descent solver to compute the required quadrature samples. Our method is verified with a CMOS ring oscillator and an optical ring resonator, showing 3000x speedup over Monte Carlo.