Fast data-driven model reduction for nonlinear dynamical systems

Abstract We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling SSMLearn uses implicit optimization to fit submanifold data and reduce dynamics normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, provide novel timelag selection when delay-embedding signals from multimodal systems. show that our alternative approach SSM construction yields accurate sparse rigorous models essentially (or non-linearizable ) on both numerical experimental datasets. Aside major in complexity, new allows an increase training dimensionality by several orders magnitude. This promises extend data-driven, SSM-based with hundreds thousands degrees freedom.