Application of a mixed variable physics-informed neural network to solve the incompressible steady-state and transient mass, momentum, and energy conservation equations for flow over in-line heated tubes

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.