We introduce a novel machine learning method called the Penalized Profile Support Vector Machine based on the Gabriel edited set for the computation of the probability of failure for a complex system as determined by a threshold condition on a computer model of system behavior. The method is designed to minimize the number of evaluations of the computer model while preserving the geometry of the decision boundary that determines the probability. It employs an adaptive sampling strategy designed to strategically allocate points near the boundary determining failure and builds a locally linear surrogate boundary that remains consistent with its geometry by strategic clustering of training points. We prove two convergence results and we compare the performance of the method against a number of state of the art classification methods on four test problems. We also apply the method to determine the probability of survival using the Lotka--Volterra model for competing species.

翻译：本文提出一种名为基于Gabriel编辑集的惩罚化轮廓支持向量机的新型机器学习方法，用于计算复杂系统的失效概率，该概率由系统行为计算机模型的阈值条件决定。该方法旨在最小化计算机模型的评估次数，同时保持决定概率的决策边界几何结构。它采用自适应采样策略，在决定失效的边界附近策略性地分配采样点，并通过训练点的策略性聚类构建与原始几何保持一致的局部线性代理边界。我们证明了两个收敛性结果，并在四个测试问题上将本方法与多种先进分类方法进行性能比较。同时，我们将该方法应用于通过Lotka--Volterra竞争物种模型确定生存概率的场景。