Navier Stokes

The Navier-Stokes equations describe fluid motion, a fundamental problem across numerous scientific and engineering disciplines. Current research focuses on developing efficient and accurate numerical solutions, particularly using machine learning techniques such as physics-informed neural networks (PINNs), deep operator networks, and graph neural networks, often incorporating techniques like adaptive time stepping and data augmentation to improve performance. These advancements aim to reduce computational costs and enhance the predictive capabilities for complex fluid flows, impacting fields ranging from weather forecasting to aerodynamic design and biomedical fluid dynamics.