<ul data-eligibleForWebStory="false"><li>Researchers have introduced a data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) to learn quadratic representations of highly nonlinear dynamical systems.</li><li>QENDy aims to identify the governing equations by embedding the system into a higher-dimensional feature space where the dynamics become quadratic, similar to SINDy (Sparse Identification of Nonlinear Dynamics).</li><li>The method requires trajectory data, time derivatives for training data points, and a set of preselected basis functions, called a dictionary. Its effectiveness was demonstrated through benchmark problems and comparison with SINDy and deep learning.</li><li>The study also analyzed the convergence of QENDy and SINDy in the infinite data limit, highlighting similarities and differences, and compared the quadratic embedding with linearization techniques based on the Koopman operator.</li></ul>

Data-driven system identification using quadratic embeddings of nonlinear dynamics

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