The Principle of Minimum Pressure Gradient: An Alternative Basis for Physics-Informed Learning of Incompressible Fluid Mechanics
arXiv:2401.07489 · doi:10.1063/5.0197860
Abstract
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.
References in corpus (11)
- Adam: A Method for Stochastic Optimization
- Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
- Activation Functions: Comparison of trends in Practice and Research for Deep Learning
- Physics-informed neural networks for inverse problems in nano-optics and metamaterials
- Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
- Physics-informed neural networks for solving Reynolds-averaged Navier$\unicode{x2013}$Stokes equations
- Machine Learning in Aerodynamic Shape Optimization
- Physics-informed deep learning for incompressible laminar flows
- Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
- Deep learning of free boundary and Stefan problems
- The Principle of Minimum Pressure Gradient: An Alternative Basis for Physics-Informed Learning of Incompressible Fluid Mechanics