Are Artificial Neural Networks suitable for data-driven moment matching?

We investigate the use of artificial neural networks in the context of data-driven moment matching for nonlinear systems, comparing it with state-of-the-art approaches that rely on regularized kernel methods or least squares. We propose a novel neural network model that shares the properties of the moment function of a nonlinear system, which can be learned by means of surrogate-based black-box optimization methods (such as Bayesian optimization). To validate the proposed approach, we conduct an extensive simulation analysis of the method on two benchmark model reduction problems, employing different settings and comparing with state-of-the-art methods. This investigation suggests that neural networks are a suitable and promising approach for data-driven moment matching, and they appear to show comparable performance to state-of-the-art methods based on regularized kernel methods.