Farid Maor
Leo AI Inc., 160 Alewife Brook Parkway, Suite 1095, Cambridge, Massachusetts 02138, USA and Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel.
Chaos. 2024 Dec 1;34(12). doi: 10.1063/5.0173938.
Data-Driven Response Regime Exploration and Identification (DR2EI) is a novel and fully data-driven method for identifying and classifying response regimes of a dynamical system without requiring human intervention. This approach is a valuable tool for exploring and discovering response regimes in complex dynamical systems, especially when the governing equations and the number of distinct response regimes are unknown, and the system is expensive to sample. Additionally, the method is useful for order reduction, as it can be used to identify the most dominant response regimes of a given dynamical system. DR2EI utilizes unsupervised learning algorithms to transform the system's response into an embedding space that facilitates regime classification. An active sequential sampling approach based on Gaussian Process Regression is used to efficiently sample the parameter space, quantify uncertainty, and provide optimal trade-offs between exploration and exploitation. The performance of the DR2EI method was evaluated by analyzing three established dynamical systems: the mathematical pendulum, the Lorenz system, and the Duffing oscillator, and its robustness to noise was validated across a range of noise magnitudes. The method was shown to effectively identify a variety of response regimes with both similar and distinct topological features and frequency content, demonstrating its versatility in capturing a wide range of behaviors. While it may not be possible to guarantee that all possible regimes will be identified, the method provides an automated and efficient means for exploring the parameter space of a dynamical system and identifying its underlying "sufficiently dominant" response regimes without prior knowledge of the system's equations or behavior.
数据驱动的响应机制探索与识别（DR2EI）是一种全新的、完全数据驱动的方法，用于识别和分类动态系统的响应机制，无需人工干预。这种方法是探索和发现复杂动态系统中响应机制的宝贵工具，特别是在控制方程和不同响应机制的数量未知且系统采样成本高昂的情况下。此外，该方法对于降阶也很有用，因为它可用于识别给定动态系统中最主要的响应机制。DR2EI利用无监督学习算法将系统的响应转换到一个便于机制分类的嵌入空间。基于高斯过程回归的主动序贯采样方法用于有效地对参数空间进行采样、量化不确定性，并在探索和利用之间提供最佳权衡。通过分析三个已建立的动态系统：数学摆、洛伦兹系统和杜芬振子，评估了DR2EI方法的性能，并在一系列噪声幅度范围内验证了其对噪声的鲁棒性。结果表明，该方法能够有效地识别具有相似和不同拓扑特征及频率内容的各种响应机制，证明了其在捕捉广泛行为方面的通用性。虽然可能无法保证识别出所有可能的机制，但该方法提供了一种自动化且高效的手段，用于探索动态系统的参数空间并识别其潜在的“充分主导”响应机制，而无需事先了解系统的方程或行为。
