随机多项式混沌展开法仿真随机模拟器
Stochastic polynomial chaos expansions to emulate stochastic simulators
摘要：
在不确定性量化的背景下，需要对计算模型进行重复评估。对于昂贵的数值模型来说，这项任务是棘手的。对于随机模拟器来说，这样的问题变得更加严重，随机模拟器的输出是给定输入参数集的随机变量。为了减轻计算负担，代理模型通常被构造和评估。然而，由于模型响应的随机性，经典的代理模型不能直接应用于随机模拟器的仿真。为了有效地表示任何给定的输入值的模型输出的概率分布，我们开发了一个新的随机代理模型称为随机多项式混沌扩展。为此，我们引入了一个潜在的变量和一个额外的噪声变量，在定义良好的输入变量，重现随机性。因此，对于给定的输入参数集，模型输出由具有加性噪声的潜在变量的函数给出，因此是随机变量。在本文中，我们提出了一种自适应算法，它不需要重复运行的模拟器相同的输入参数。所提出的方法的性能进行了比较与广义λ模型和一个国家的最先进的核估计的两个案例研究，在数学金融和流行病学和一个分析的例子，其响应分布是双峰。结果表明，该方法能够准确地表示一般的响应分布，即，不仅是正常的或单峰的。在精度方面，它通常优于广义lambda模型和核密度估计。
英文摘要：
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the output of which is a random variable for a given set of input parameters. To alleviate the computational burden, surrogate models are usually constructed and evaluated instead. However, due to the random nature of the model response, classical surrogate models cannot be applied directly to the emulation of stochastic simulators. To efficiently represent the probability distribution of the model output for any given input values, we develop a new stochastic surrogate model called stochastic polynomial chaos expansions. To this aim, we introduce a latent variable and an additional noise variable, on top of the well-defined input variables, to reproduce the stochasticity. As a result, for a given set of input parameters, the model output is given by a function of the latent variable with an additive noise, thus a random variable. In this paper, we propose an adaptive algorithm which does not require repeated runs of the simulator for the same input parameters. The performance of the proposed method is compared with the generalized lambda model and a state-of-the-art kernel estimator on two case studies in mathematical finance and epidemiology and on an analytical example whose response distribution is bimodal. The results show that the proposed method is able to accurately represent general response distributions, i.e., not only normal or unimodal ones. In terms of accuracy, it generally outperforms both the generalized lambda model and the kernel density estimator.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
