  We use Koopman theory to develop a data-driven nonlinear model reduction and
identification strategy for multiple-input multiple-output (MIMO) input-affine
dynamical systems. While the present literature has focused on linear and
bilinear Koopman models, we derive and use a Wiener-type Koopman formulation.
We discuss that the Wiener structure is particularly suitable for model
reduction, and can be naturally derived from Koopman theory. Moreover, the
Wiener block-structure unifies the mathematical simplicity of linear dynamical
blocks and the accuracy of bilinear dynamics. We present a Koopman
deep-learning strategy combining autoencoders and linear dynamics that
generates low-order surrogate models of MIMO Wiener type. In three case
studies, we apply our framework for identification and reduction of a system
with input multiplicity, a chemical reactor and a high-purity distillation
column. We compare the prediction performance of the identified Wiener models
to linear and bilinear Koopman models. We observe the highest accuracy and
strongest model reduction capabilities of low-order Wiener-type Koopman models,
making them promising for control.
