A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

TL;DR

This paper introduces an accelerated multicanonical Monte Carlo method using Gaussian process surrogates to efficiently estimate the probability density function in uncertainty quantification problems, significantly speeding up computations.

Contribution

The paper develops an adaptive surrogate-accelerated MMC algorithm that enhances efficiency in estimating PDFs for uncertain systems, outperforming standard Monte Carlo methods.

Findings

Achieves several orders of magnitude speedup over standard Monte Carlo

Effectively constructs local Gaussian process surrogates for acceleration

Demonstrates efficiency through numerical examples

Abstract

In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter $y$. The performance parameter $y$ is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of $y$. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithm, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo method.