Efficient Propagation of Uncertainty via Reordering Monte Carlo Samples

TL;DR

This paper introduces an adaptive reordering method for Monte Carlo samples to improve the efficiency of uncertainty propagation in computational models, reducing the number of samples needed for accurate results.

Contribution

The paper proposes a novel adaptive reordering technique for Monte Carlo samples that accelerates uncertainty propagation, especially for computationally expensive models.

Findings

Reordering MC samples enhances convergence speed.

The method reduces computational costs of uncertainty analysis.

Improves efficiency of uncertainty propagation in complex models.

Abstract

Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine model output uncertainties based on the uncertainty in its input variables. The most common and simplest approach to propagate the uncertainty from a model inputs to its outputs is by feeding a large number of samples to the model, known as Monte Carlo (MC) simulation which requires exhaustive sampling from the input variable distributions. However, MC simulations are impractical when models are computationally expensive. In this work, we investigate the hypothesis that while all samples are useful on average, some samples must be more useful than others. Thus, reordering MC samples and propagating more useful samples can lead to enhanced convergence in statistics of interest earlier and thus, reducing the computational burden of UP process. Here, we introduce a methodology to adaptively reorder MC samples and show how it results in reduction of computational expense of UP processes.