Variationally mimetic operator network approach to transient viscous flows
This work applies an existing operator network method to a new domain (transient viscous flows), which is incremental for researchers in computational fluid dynamics.
The authors extended the VarMiON machine learning method to predict transient viscous flows at low-to-moderate Reynolds numbers, achieving very good agreement with finite-element reference solutions in three test geometries.
The Variationally Mimetic Operator Network (VarMiON) approach is a machine learning technique, originally developed to predict the solution of elliptic differential problems, that combines operator networks with a structure inherited from the variational formulation of the equations. We investigate the capabilities of this method in the context of viscous flows, by extending its formulation to vector-valued unknown fields and with a particular emphasis on the space-time approximation context necessary to deal with transient flows. As a first step, we restrict attention to the regime of low-to-moderate Reynolds numbers, in which the Navier--Stokes equations can be linearized to give the time-dependent Stokes problem for incompressible fluids. The details of the method as well as its performance are illustrated in three paradigmatic flow geometries where we obtain a very good agreement between the VarMiON predictions and reference finite-element solutions.