Interconnected data arising from networks such as data from social, biological, molecular, sensor and financial networks come on massive amoint and carry hidden information in their structure that can be key to identify fake news, discover new drugs, identify malfunctioning sensor, and making useful recommendations. Sucessfully solving this task requires building learning tools capable of leveraging the underlying structure so as to map the information in meaningul embeddings.

Graph neural networks (GNNs) extend the sucess of deep learning from text, speech and images to graph-based data and allow extracting informtion in a similar layere fashion. They have shown wide sucess in all the aforementioned applications but there is still a lot to do to improve them further as well as our understanding on their inner-working mechanisms.

MSc thesis topics: Master projects in this category will concern foundamental research into the inner work mechanisms of GNNs. Particular areas include:

• Dynamic graphs: Many real-world graphs change over time but yet current solutions sledomly work on this setting. In this project, you will focus on developing GNNs that can process data on graphs whose edges/nodes appear but could also focus on analysing the limitations of existing solutions.

• Physic-informed GNNs: Current GNN solutions do not rely on any physical model to process their data. However, expoiting prior physical laws on graphs it is not only possible to build better GNNs solutions but to also provide a deeper understanding on their inner-workings. Topics on this thesis will center around the intersection of these two areas.

• Self-supervised learning (SSL): SSL aims at leveraging unlabeled data to train a network. However, how to perform SSL on graphs is not well understood. Your task would be mainly centered on developing novel SSL approaches for graph learning.

Time series on networks are commonly encountered in weather sensor networks, finance, and biological networks. Therefore, modeling and analyzing the effects of time varying network signals is a topic of high importance to detect malfunctioning sensors, predict stock prices as well as monitor biological activities. For example,  we can represent sensors as nodes of a graph and communications links as edges. The temperature measured in each sensor is a signal residing on the nodes on this graph, where the signal temporal evolution is dictated by the underlying topology. However, the effects of a temperature change in adjacent nodes are difficult to model with conventional techniques. Recent techniques from graoh machine learning can be an effective way to process time varying signals on networks. These models exploit graph neural networks and the structure of the data over time to aid modeling.

MSc thesis topic: In this master project, your task is to model the time varying signals via graph machine learning models. Two important questions to answer are: i) How to build an effective graph structure for modeling the underlying network? ii) How to exploit this network and graph filters to model the signal temporal evolution? You will work on both theoretical and practical aspects of the project and will compare your algorithm with different baselines models. Topic inspiration from the research on GNNs can be adopted here but the dynamci nature of the data makes everything more intruguing as we need now to capture both the data relation over the graph and time.

• Online learning: When the data come in a streaming fashion, we want to train our model on the fly. However, how to best incorporate the latter is not well-known. Also, we want to characterize the impact of this online learning on the overall performance.

• Physic-based learning: In this project, we want to mix physical models with graph-time models to learn from the temporal evolution of the data. The mix physical models allow us to also obtain more interpretable and data efficient solutions. Characterizing the role of the latter is could also be an interesting thsis topic.