  We develop a model reduction technique for non-smooth dynamical systems using
spectral submanifolds. Specifically, we construct low-dimensional, sparse,
nonlinear and non-smooth models on unions of slow and attracting spectral
submanifolds (SSMs) for each smooth subregion of the phase space and then
properly match them. We apply this methodology to both equation-driven and
data-driven problems, with and without external forcing.
