Graph neural networks and Physics

📝 Description

This is a project focused on the theoretical aspects, involving some maths with graph theory and machine learning and some Python programming.

The idea is to get inspiration from Physics to design new neural network achitectures. The Laplacian is an operator that is present in Partial Differential Equations and also in graphs. Through this connection we can build new graph neural network achitectures inspired by Physics and inheriting some properties of partial differential equations. The connection between Physics and Machine Learning is a growing and promising direction of research. Some recent studies relates differential equations and graphs Graph neural diffusion and neural diffusion and beyond. Moreover, interesting results were found by Tobias Antonsen during his Master project at UiT (Propagating information like waves in GNNs). We want to continue in this direction, exploring other physics equations, possibly related to fuild mechanics and test our models on different datasets, with noisy data.

📚 References:

• Graph neural diffusion
• neural diffusion and beyond
• Propagating information like waves in GNNs

📨 Contact:

Benjamin Ricaud benjamin.ricaud@uit.no