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The prohibitive cost and low fidelity of experimental data in industry scalethermofluid systems limit the usefulness of pure data-driven machine learningmethods. Physics-informed neural networks (PINN) strive to overcome this byembedding the physics equations in the construction of the neural network lossfunction. In the present paper, the mixed-variable PINN methodology is appliedto develop steady-state and transient surrogate models of incompressiblelaminar flow with heat transfer through a 2D internal domain with obstructions.Automatic spatial and temporal differentiation is applied to the partialdifferential equations for mass, momentum and energy conservation, and theresiduals are included in the loss function, together with the boundary andinitial values. Good agreement is obtained between the PINN and CFD results forboth the steady-state and transient cases, but normalization of the PDEs provesto be crucial. Although this proves the ability of the PINN approach to solvemultiple physics-based PDEs on a single domain, the PINN takes significantlylonger to solve than the traditional finite volume numerical methods utilizedin commercial CFD software.

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