Uncertainty quantification of engineering problems using N-body system designs: An overview

When conducting an uncertainty quantification of computationally intensive models, it is vital that the realizations of the input random variables are consciously selected so that completing of each simulation yields as much new information as possible. To achieve that, a great effort is invested into optimization of uniformity of input sampling points across the design domain. The purpose of this paper is threefold: (i) it provides a review of design optimality criteria, with a focus on distance-based criteria that can be viewed in analogy to N-body systems, and includes comparisons to low-discrepancy designs; (ii) it documents, for the first time, that point samples obtained using the authors’ previously developed N-body optimization algorithm Vořechovský et al. (2019), Vořechovský and Mašek (2020) exhibit exceptional uniformity and outperform samples generated by existing methods; and (iii) it explains potential pitfalls of applying N-body analogies too naively — such as neglecting energetic considerations, dimension scaling, and domain boundaries — as well as identifies opportunities for efficient computational implementation. We demonstrate that using these optimized designs in numerical analyses, both in research and engineering practice, leads to either a substantial increase in estimation precision or a reduction in the number of model runs required to achieve a desired estimation error. The performance of the constructed point samples is compared to the sampling methods that are today considered as go-to sampling strategies by researchers and practicing engineers. It is demonstrated that the proposed optimization method is superior to the state-of-the art methods in both robustness as well as estimation error (variance reduction). Inherent limitations for vast point samples posed by a finite computing power are also discussed. • Sample uniformity optimization using an N-body system. • Exceptional performance and robustness within Monte Carlo integration. • Parallelized implementation. • Modifications for spatial and statistical uniformity of samples. • Mitigation of the influence of high sample dimension and low domain saturation.