论文标题
分位数集反转计算机实验的贝叶斯顺序设计
Bayesian sequential design of computer experiments for quantile set inversion
论文作者
论文摘要
我们考虑一个未知的多元函数，代表系统类似于确定性和不确定输入的复杂数值模拟器。我们的目标是估计一组确定性输入，导致属于给定集的概率（相对于不确定输入的分布）的输出小于给定阈值。我们称此问题称之为分位数集反转（QSI），例如在健壮（基于可靠性的）优化问题的背景下，在寻找以足够大概率满足约束的解决方案时。 为了解决QSI问题，我们根据高斯过程建模和逐步的不确定性降低（SUR）原理提出了贝叶斯策略，以顺序选择应评估该函数的点以有效地近似关注集。我们通过几个数值实验来说明拟议的SUR策略的性能和兴趣。
We consider an unknown multivariate function representing a system-such as a complex numerical simulator-taking both deterministic and uncertain inputs. Our objective is to estimate the set of deterministic inputs leading to outputs whose probability (with respect to the distribution of the uncertain inputs) of belonging to a given set is less than a given threshold. This problem, which we call Quantile Set Inversion (QSI), occurs for instance in the context of robust (reliability-based) optimization problems, when looking for the set of solutions that satisfy the constraints with sufficiently large probability. To solve the QSI problem we propose a Bayesian strategy, based on Gaussian process modeling and the Stepwise Uncertainty Reduction (SUR) principle, to sequentially choose the points at which the function should be evaluated to efficiently approximate the set of interest. We illustrate the performance and interest of the proposed SUR strategy through several numerical experiments.
