Multi-Fidelity Machine Learning Applied to Steady Fluid Flows

TL;DR

This paper introduces a machine learning approach that predicts steady fluid flows using elliptic boundary features, enabling accurate modeling with minimal high-fidelity data and improving CFD solver efficiency.

Contribution

The method uses elliptic boundary value solutions as input features, allowing generalization across boundary geometries with limited high-fidelity data, and employs adaptive sampling for training.

Findings

Accurately predicts steady flow fields around cylinders and airfoils.

Reduces CFD solver convergence time by using ML-predicted flow fields as initial conditions.

Requires only one high-fidelity simulation for effective modeling.

Abstract

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to boundary geometry by using solutions to elliptic boundary value problems over the flow domain as the model input, instead of Cartesian coordinates of the domain. Training data is generated through pointwise evaluation of flow features at points selected through a quad-tree adaptive sampling method to concentrate training points in areas with large field gradients. Models are trained within a training window around the body, while predictions are smoothly extended to freestream conditions using a Partition-of-Unity extension. Predictive capabilities of the machine learning model are demonstrated in steady-state flow of incompressible fluid around a cylinder and a Joukowski airfoil. The predicted flow field is used to warm-start CFD simulations to achieve acceleration in solver convergence.