用少次数模拟计算复杂系统失效概率，精度高且结果可解释。
An efficient, accurate, and interpretable machine learning method for computing probability of failure
- 基于格拉贝尔编辑集的惩罚轮廓支持向量机，自适应聚焦边界区域采样。
- 仅需少量模型评估即逼近真实失效概率，收敛性有理论保证。
- 适合高成本仿真系统的可靠性分析，尤其看重可解释性的场景。
我们提出一种名为基于格拉贝尔编辑集的惩罚轮廓支持向量机的新机器学习方法，用于计算由计算机模型行为阈值条件决定的复杂系统失效概率。该方法旨在最小化计算机模型的评估次数，同时保持决定失效概率的决策边界的几何特性。通过自适应采样策略，将采样点集中在决定失效的边界附近，并构建局部线性代理边界，通过训练点的智能聚类保持其几何一致性。我们证明了两个收敛性结果，并在四个测试问题上与多种先进分类方法进行了性能对比。此外，还将该方法应用于使用洛特卡-沃尔泰拉模型模拟竞争物种生存概率的问题。
原文摘要 · Abstract (English)
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.
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