  We present a fast method for nonlinear data-driven model reduction of
dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs).
We use observed data to locate a low-dimensional, attracting slow SSM and
compute a maximally sparse approximation to the reduced dynamics on it. The
recently released SSMLearn algorithm uses implicit optimization to fit a
spectral submanifold to data and reduce the dynamics to the normal form. Here,
we present two simplified algorithms, which reformulate manifold fitting and
normal form computation as explicit problems under certain assumptions. We show
on both numerical and experimental datasets that these algorithms yield
accurate and sparse rigorous models for essentially nonlinear (or
non-linearizable) dynamics. The new algorithms are significantly simplified and
provide a speedup of several orders of magnitude.
