  This work presents a non-intrusive model reduction method to learn
low-dimensional models of dynamical systems with non-polynomial nonlinear terms
that are spatially local and that are given in analytic form. In contrast to
state-of-the-art model reduction methods that are intrusive and thus require
full knowledge of the governing equations and the operators of a full model of
the discretized dynamical system, the proposed approach requires only the
non-polynomial terms in analytic form and learns the rest of the dynamics from
snapshots computed with a potentially black-box full-model solver. The proposed
method learns operators for the linear and polynomially nonlinear dynamics via
a least-squares problem, where the given non-polynomial terms are incorporated
in the right-hand side. The least-squares problem is linear and thus can be
solved efficiently in practice. The proposed method is demonstrated on three
problems governed by partial differential equations, namely the
diffusion-reaction Chafee-Infante model, a tubular reactor model for reactive
flows, and a batch-chromatography model that describes a chemical separation
process. The numerical results provide evidence that the proposed approach
learns reduced models that achieve comparable accuracy as models constructed
with state-of-the-art intrusive model reduction methods that require full
knowledge of the governing equations.
