Data-Driven Model Identification Using Time Delayed Nonlinear Maps for Systems with Multiple Attractors

TL;DR

This paper introduces a novel data-driven approach for identifying complex dynamical systems with multiple attractors using time delayed nonlinear maps, enhancing accuracy and applicability across scientific fields.

Contribution

The study develops a new method leveraging time delay and nonlinear maps for system identification, improving upon traditional embedding techniques for systems with multiple attractors.

Findings

Enhanced training and testing strategies for operator learning.

Effective assessment of algorithmic accuracy and expressibility.

Broad applicability across scientific and engineering domains.

Abstract

This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as attractors and their basins. By understanding these structures, we have improved training and testing strategies for operator learning and system identification. Our method uses time delay and non-linear maps rather than embeddings, enabling the assessment of algorithmic accuracy and expressibility, particularly in systems exhibiting multiple attractors. This method, along with its associated algorithm and computational framework, offers broad applicability across various scientific and engineering domains, providing a useful tool for data-driven characterization of systems with complex nonlinear system dynamics.