Uncertainty quantification (UQ) is an active area of research, and an essential technique used in all fields of science and engineering. The most common methods for UQ are Monte Carlo and surrogate-modelling. The former method is dimensionality independent but has slow convergence, while the latter method has been shown to yield large computational speedups with respect to Monte Carlo. However, surrogate models suffer from the so-called curse of dimensionality, and become costly to train for high-dimensional problems, where UQ might become computationally prohibitive. In this paper we present a new technique, Lasso Monte Carlo (LMC), which combines a Lasso surrogate model with the multifidelity Monte Carlo technique, in order to perform UQ in high-dimensional settings, at a reduced computational cost. We provide mathematical guarantees for the unbiasedness of the method, and show that LMC can be more accurate than simple Monte Carlo. The theory is numerically tested with benchmarks on toy problems, as well as on a real example of UQ from the field of nuclear engineering. In all presented examples LMC is more accurate than simple Monte Carlo and other multifidelity methods. Thanks to LMC, computational costs are reduced by more than a factor of 5 with respect to simple MC, in relevant cases.

翻译：不确定性量化（UQ）是研究活跃领域，也是科学与工程各领域不可或缺的技术。最常用的UQ方法包括蒙特卡洛法和替代模型法：前者具有维度无关性但收敛速度慢，后者虽能显著提升计算效率（相对于蒙特卡洛法），却面临"维度灾难"问题——在高维问题中，替代模型训练成本高昂，导致UQ计算可能变得不可行。本文提出一种新技术——Lasso蒙特卡洛（LMC），该方法将Lasso替代模型与多保真度蒙特卡洛技术相结合，旨在以降低的计算成本实现高维环境下的UQ。我们为该方法的无偏性提供了数学证明，并展示LMC可达到优于简单蒙特卡洛法的精度。通过玩具问题基准测试及核工程领域真实UQ案例的数值验证，所有示例均表明LMC精度优于简单蒙特卡洛法及其他多保真度方法。在相关场景中，相较于简单蒙特卡洛法，LMC可将计算成本降低超过5倍。