Efficient Propagation of Uncertainty via Reordering Monte Carlo Samples
This work addresses the problem of computational inefficiency in uncertainty propagation for decision-based material design, representing an incremental improvement over standard Monte Carlo methods.
The paper tackles the computational burden of Monte Carlo simulations for uncertainty propagation in expensive models by proposing an adaptive reordering of samples to enhance convergence of statistics earlier, resulting in reduced computational expense.
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.