2019/11/20 by Xiao Zhu, Zhu, X., Bruno Sudret +1 · 2 citations
Computer Science · Decision Sciences · #Advanced Multi-Objective Optimization Algorithms #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (stat.ML) #Probabilistic and Robust Engineering Design #Simulation Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1911.09067
openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random variable with unknown probability density function (PDF). Of interest in this paper is the construction of a surrogate that can accurately predict this response PDF for any input parameters. We suggest using a flexible distribution family -- the generalized lambda distribution -- to approximate the response PDF. The associated distribution parameters are cast as functions of input parameters and represented by sparse polynomial chaos expansions. To build such a surrogate model, we propose an approach based on a local inference of the response PDF at each point of the experimental design based on replicated model evaluations. Two versions of this framework are proposed and compared on analytical examples and case studies.