Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.02124 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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.