The Principle of Minimum Pressure Gradient: An Alternative Basis for Physics-Informed Learning of Incompressible Fluid Mechanics
This work addresses computational efficiency for researchers in fluid mechanics, but it is incremental as it offers an alternative method rather than a breakthrough.
The paper tackles the problem of physics-informed learning for incompressible fluid mechanics by proposing a variational method based on the principle of minimum pressure gradient, which reduces computational time per training epoch compared to conventional Navier-Stokes-based approaches.
Recent advances in the application of physics-informed learning into the field of fluid mechanics have been predominantly grounded in the Newtonian framework, primarly leveraging Navier-Stokes Equation or one of its various derivative 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.