A. Longa: A hands-on introduction to Graph Deep Learning, with examples in PyTorch Geometric (2/4)

Abstract: Neural Networks and Deep Learning have started only recently to become standard tools in simulation and computational sciences, and they have already enabled significant advances, becoming a viable option for the data-driven solution of possibly high-dimensional and parametric PDEs.
In the deep learning literature, recent years have seen a growing interest for the development of Graph Neural Networks (GNNs), which are deep learning techniques applicable to graph-structured inputs. This field is particularly relevant to address the typical mesh-based problems that are often encountered in the numerical solution of PDEs, and indeed initial results in this direction are being investigated. The aim of this series of seminars is to provide an hands-on introduction to this novel field of machine learning. We will recall some basic facts on graph theory, introduce the fundamental ideas underlying the functioning of GNNs and describe their common mathematical formulation, and provide several concrete examples of the most common GNN layers. After these introductory part, the seminars will cover the following topics:
• Implementation of GNNs: How to implement a full GNN pipeline in PyTorch Geometric, which is a standard library for GNNs in Python.
• Explainability of GNNs: How to inspect a model to try to understand the learned decision pattern.
• Heterogeneity in GNNs: How can GNNs effectively model and incorporate a diversity of nodes and edges with different types.
At the end of the tutorial, the audience will be able to load custom graph-based data and train simple GNN models for regression and classification of nodes and graphs, and to inspect them under different conditions.