  We present a novel method for learning reduced-order models of dynamical
systems using nonlinear manifolds. First, we learn the manifold by identifying
nonlinear structure in the data through a general representation learning
problem. The proposed approach is driven by embeddings of low-order polynomial
form. A projection onto the nonlinear manifold reveals the algebraic structure
of the reduced-space system that governs the problem of interest. The matrix
operators of the reduced-order model are then inferred from the data using
operator inference. Numerical experiments on a number of nonlinear problems
demonstrate the generalizability of the methodology and the increase in
accuracy that can be obtained over reduced-order modeling methods that employ a
linear subspace approximation.
