A Model-Free Sampling Method for Estimating Basins of Attraction Using Hybrid Active Learning (HAL)
This addresses the challenge of determining basins of attraction in experimental or model-unknown scenarios, which is incremental as it builds on active learning techniques for a specific domain.
The paper tackles the problem of estimating basins of attraction for nonlinear systems without requiring a known dynamical model, introducing a model-free sampling method based on hybrid active learning that efficiently determines BoA boundaries, as demonstrated with high efficiency in a bistable nonlinear system example.
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.