Scale-invariant Monte Carlo and multilevel Monte Carlo estimation of mean and variance: An application to simulation of linear elastic bone tissue

TL;DR

This paper introduces scale-invariant error estimators for Monte Carlo methods that optimize computational cost across fidelities, demonstrated on a bone tissue simulation with uncertain material properties.

Contribution

It presents novel, dimensionless error estimators for Monte Carlo and multilevel Monte Carlo methods that are robust to distribution variations.

Findings

Error estimators are fully dimensionless and robust.

Algorithms effectively optimize computation in bone tissue simulation.

Application demonstrates improved efficiency in uncertain material modeling.

Abstract

We propose novel scale-invariant error estimators for the Monte Carlo and multilevel Monte Carlo estimation of mean and variance. For any linear transformation of the distribution of the quantity of interest, the computation cost across fidelity levels is optimized using a normalized error estimate, which is not only fully dimensionless but also remains robust to variation in characteristics of the distribution. We demonstrate the effectiveness of the algorithms through application to a mechanical simulation of linear elastic bone tissue, where material uncertainty incorporating both heterogeneity and random anisotropy is considered in the constitutive law.