Fluid Flow Modelling Using Physics-Informed Convolutional Neural Network in Parametrised Domains

Abstract

We design and implement a physics-informed convolutional neural network (CNN) to solve fluid flow problems on a parametrised domain. The goal is to compare the effectiveness of training based solely on CFD-generated training data with purely physics-informed training and training based on a combination of both. We consider the problem of incompressible fluid flow in a convergent-divergent channel with variable wall shape. A speciality of the designed neural network is the incorporation of the boundary condition directly in the CNN. A physics-informed CNN that uses a non-Cartesian mesh poses a challenge when evaluating partial derivatives. We propose a gradient layer that pproximates the first and second partial derivatives by finite differences using Lagrange interpolation. Our analysis shows that the convergence of purely physics-informed training is slow. However, using a small training dataset in combination with physics-informed training can achieve results comparable to physics-uninformed training with a considerably larger training dataset.