论文标题
一种无模型抽样方法，用于使用混合活动（HAL）估算吸引盆地的盆地
A Model-Free Sampling Method for Estimating Basins of Attraction Using Hybrid Active Learning (HAL)
论文作者
论文摘要
了解吸引力的盆地（BOA）通常是非线性系统的重要考虑因素。确定高分辨率BOA的大多数现有方法需要对系统的动态模型进行先验知识（例如，连续系统的微分方程或点映射，离散系统的单元格映射等），这允许在多核计算机上衍生近似分析解决方案或并行计算，以便找到BOA有效地找到BOA。但是，当必须通过实验确定BOA或系统模型未知时，这些方法通常是不切实际的。本文介绍了BOA的无模型抽样方法。所提出的方法基于混合活动（HAL），旨在查找和标记“信息性”样本，从而有效地确定BOA的边界。它由三个主要部分组成：1）对轨迹（AST）进行附加采样，以最大化从每个模拟或实验获得的样品数量； 2）主动学习（AL）算法利用BOA的局部边界； 3）一种基于密度的采样（DB）方法，用于探索BOA的整体边界。提出了估计双轴向非线性系统的BOA的一个示例，以显示我们HAL采样方法的高效率。
Understanding the basins of attraction (BoA) is often a paramount consideration for nonlinear systems. Most existing approaches to determining a high-resolution BoA require prior knowledge of the system's dynamical model (e.g., differential equation or point mapping for continuous systems, cell mapping for discrete systems, etc.), which allows derivation of approximate analytical solutions or parallel computing on a multi-core computer to find the BoA efficiently. However, these methods are typically impractical when the BoA must be determined experimentally or when the system's model is unknown. This paper introduces a model-free sampling method for BoA. The proposed method is based upon hybrid active learning (HAL) and is designed to find and label the "informative" samples, which efficiently determine the boundary of BoA. It consists of three primary parts: 1) additional sampling on trajectories (AST) to maximize the number of samples obtained from each simulation or experiment; 2) an active learning (AL) algorithm to exploit the local boundary of BoA; and 3) a density-based sampling (DBS) method to explore the global boundary of BoA. An example of estimating the BoA for a bistable nonlinear system is presented to show the high efficiency of our HAL sampling method.
