The principle of minimum pressure gradient: An alternative basis for physics-informed learning of incompressible fluid mechanics

Recent advances in the application of physics-informed learning in the field of fluid mechanics have been predominantly grounded in the Newtonian framework, primarily leveraging Navier-Stokes equations or one of their various derivatives to train a neural network. Here, we propose an alternative approach based on variational methods. The proposed approach uses the principle of minimum pressure gradient combined with the continuity constraint to train a neural network and predict the flow field in incompressible fluids. We describe the underlying principles of the proposed approach, then use a demonstrative example to illustrate its implementation, and show that it reduces the computational time per training epoch when compared to the conventional approach.