Hysteresis and Nonlinear Dynamical Systems Modeling

The field of nonlinear dynamical systems is moving towards the development of more advanced and flexible modeling techniques. Recent research has focused on addressing the challenges of modeling complex systems with nonlinear phenomena, such as hysteresis, and high-dimensional dynamics. A key direction is the integration of machine learning and symbolic regression to automatically discover governing equations and extract internal variables, enabling more accurate predictions and characterizations of these systems. Another important area of research is the development of methods that can implicitly learn latent dynamics and produce interpretable representations, which is crucial for long-horizon dynamical prediction and control. Noteworthy papers include: A unified framework for equation discovery and dynamic prediction of hysteretic systems, which develops a systematic approach for modeling hysteresis. KALIKO: Kalman-Implicit Koopman Operator Learning For Prediction of Nonlinear Dynamical Systems, which presents a method that leverages the Kalman filter to implicitly learn embeddings corresponding to latent dynamics.

Sources

A unified framework for equation discovery and dynamic prediction of hysteretic systems

KALIKO: Kalman-Implicit Koopman Operator Learning For Prediction of Nonlinear Dynamical Systems

Data-driven Methods for Delay Differential Equations

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