Machine Learning Applications in Linear and Non-Linear Dynamics

Abstract

Machine learning (ML) applications in linear and nonlinear dynamics represent a burgeoning field with significant implications for understanding, predicting, and controlling complex systems’ behavior. Linear and nonlinear dynamics govern the behavior of diverse systems, ranging from mechanical structures to biological processes, and understanding their dynamics is crucial for various scientific and engineering applications [1-5]. In recent years, machine learning techniques have been increasingly applied to linear and nonlinear dynamics to address challenges such as modeling complexity, parameter estimation, system identification, and predictive analysis. By leveraging vast amounts of data and powerful algorithms, machine learning enables the extraction of meaningful patterns, relationships, and insights from complex dynamical systems [2]. This introduction sets the stage for exploring the diverse applications of machine learning in linear and nonlinear dynamics, including time series prediction, system identification, model validation, control design, and optimization. By integrating machine learning with dynamical systems theory, researchers and engineers can unlock new capabilities for analyzing and manipulating complex systems, leading to advancements in fields such as robotics, aerospace engineering, biomedicine, and climate science