Application of mixed-variable physics-informed neural networks to solve normalised momentum and energy transport equations for 2D internal convective flow

TL;DR

This paper demonstrates the use of mixed-variable physics-informed neural networks (PINNs) to model 2D internal convective flow, effectively solving coupled PDEs for momentum and energy with good accuracy, but with higher computational cost than traditional methods.

Contribution

The study introduces a mixed-variable PINN approach for coupled momentum and energy PDEs in 2D internal flow, emphasizing normalization and demonstrating its capability to handle multiple physics.

Findings

PINNs accurately match CFD results for steady and transient flow.

Normalization of PDEs is essential for PINN accuracy.

PINNs require longer computation times than traditional CFD methods.

Abstract

The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding the physics equations in the construction of the neural network loss function. In the present paper, the mixed-variable PINN methodology is applied to develop steady-state and transient surrogate models of incompressible laminar flow with heat transfer through a 2D internal domain with obstructions. Automatic spatial and temporal differentiation is applied to the partial differential equations for mass, momentum and energy conservation, and the residuals are included in the loss function, together with the boundary and initial values. Good agreement is obtained between the PINN and CFD results for both the steady-state and transient cases, but normalization of the PDEs proves to be crucial. Although this proves the ability of the PINN approach to solve multiple physics-based PDEs on a single domain, the PINN takes significantly longer to solve than the traditional finite volume numerical methods utilized in commercial CFD software.