The Laplacian operator can be interpreted as local message passing over graph neighborhoods, making it naturally compatible with graph neural networks. This project explores graph-based representations of spatial grids for solving Partial Differential Equations (PDEs).
- Grid generation for spatial domains
- Graph construction using k-NN
- Visualization of graph structures
- Numerical PDE solver (Laplace equation)
- Integration of graph + field values
Modern approaches like Neural Operators and Graph Neural Networks require structured graph representations of physical domains. This project builds a foundation toward such models.
Python, NumPy, Matplotlib
- Navier-Stokes simulation
- Graph Neural Networks (PyTorch Geometric)
- Fourier Neural Operators