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math.DS2023
Data-Driven Modeling and Forecasting of Chaotic Dynamics on Inertial Manifolds Constructed as Spectral Submanifolds
Aihui Liu, Joar Axås, George Haller
We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic o…
math.DS2023★ 43 cited
Nonlinear Model Reduction to Fractional and Mixed-Mode Spectral Submanifolds
George Haller, Bálint Kaszás, Aihui Liu +1
A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace of a dynamical system linearized at a fixed point. Passin…
math.DS2023
Model reduction for nonlinearizable dynamics via delay-embedded spectral submanifolds
Joar Axås, George Haller
Delay embedding is a commonly employed technique in a wide range of data-driven model reduction methods for dynamical systems, including the Dynamic mode decomposition (DMD), the H…