Physics-driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks

TL;DR

This paper introduces a physics-driven CNN approach using U-net architectures to predict steady flow fields governed by Navier-Stokes equations, achieving high accuracy and efficient training with limited data.

Contribution

The work presents a novel CNN-based method incorporating physics into the loss function for steady flow prediction, improving accuracy and training efficiency over traditional neural networks.

Findings

Achieved first-order accuracy in flow predictions.

Successfully modeled flow around a cylinder with correct vortex patterns.

Significantly accelerated training for multiple cases, especially at low Reynolds numbers.

Abstract

Recently, physics-driven deep learning methods have shown particular promise for the prediction of physical fields, especially to reduce the dependency on large amounts of pre-computed training data. In this work, we target the physics-driven learning of complex flow fields with high resolutions. We propose the use of \emph{Convolutional neural networks} (CNN) based U-net architectures to efficiently represent and reconstruct the input and output fields, respectively. By introducing Navier-Stokes equations and boundary conditions into loss functions, the physics-driven CNN is designed to predict corresponding steady flow fields directly. In particular, this prevents many of the difficulties associated with approaches employing fully connected neural networks. Several numerical experiments are conducted to investigate the behavior of the CNN approach, and the results indicate that a first-order accuracy has been achieved. Specifically for the case of a flow around a cylinder, different flow regimes can be learned and the adhered "twin-vortices" are predicted correctly. The numerical results also show that the training for multiple cases is accelerated significantly, especially for the difficult cases at low Reynolds numbers, and when limited reference solutions are used as supplementary learning targets.