# A Model-Free Sampling Method for Estimating Basins of Attraction Using Hybrid Active Learning (HAL)

arXiv: https://arxiv.org/abs/2003.10976 · HTML: https://mlsanity.com/paper/2003.10976/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2020.

## Built on by (most cited first, 4 of 4)

- [YOLO-PPA based Efficient Traffic Sign Detection for Cruise Control in Autonomous Driving](https://mlsanity.com/paper/2409.03320/) (2024)
- [AR Overlay: Training Image Pose Estimation on Curved Surface in a Synthetic Way](https://mlsanity.com/paper/2409.14577/) (2024)
- [Deep Adaptive Interest Network: Personalized Recommendation with Context-Aware Learning](https://mlsanity.com/paper/2409.02425/) (2024)
- [Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings](https://mlsanity.com/paper/2411.00989/) (2024)

## Abstract (arXiv)

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.