Using CNNs to solve Navier-Stokes Equations
Efficient simulation of the Navier-Stokes equations for fluid flow is a longstanding problem in applied mathematics, traditionally requiring substantial computational resources. However, in many scenarios, an exact solution is not necessary. Fast, real-time computations with highly realistic simulations are sufficient, such as in movies or video games.
This notebook aims to present recent and promising methods using convolutional neural networks (CNNs) to achieve fast and realistic simulations. It explains the underlying theories, the physics-based equations, their resolution using finite element methods and how can deep learning help fasten computation.
- Classic Projection Method: Understanding the foundational projection method for solving Navier-Stokes equations.
- 2013 Approach by Jonathan Tompson et al.: Accelerating Eulerian Fluid Simulation with Convolutional Networks, highlighting significant improvements in solving times.
- 2021 Approach by Nils Wandel et al.: Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D, addressing and overcoming the limitations of the earlier method.
Contributions are welcome! Please fork the repository and submit a pull request with your changes.