Learning to localize anomalies and optimize itineraries via an AI framework for combinatorial optimization in temporal graphs

Many complex systems — such as the Internet, transportation networks, and financial infrastructures — produce data that naturally takes the form of temporal graphs, where each link between nodes is time-stamped. These graphs allow us to model and analyze interactions over time, such as network traffic between computers, scheduled trips between stations, or transactions between bank accounts. A common challenge in working with such graphs is identifying subsets of the temporal graph that optimize certain properties, like densities, sizes, lengths, durations, etc., which are essential for applications such as anomaly detection, cybersecurity, and route planning. Yet, they typically involve NP-hard combinatorial problems, making them unfeasible to compute exactly on large instances.

This PhD project explores a new direction for tackling these problems using artificial intelligence. While heuristic methods exist, they often struggle to balance speed and accuracy when coping with temporal graphs. In contrast, recent advances show that AI models can be trained to solve combinatorial problems on static graphs efficiently, yet their potential remains largely unexplored in the temporal graph setting. This project aims to bridge that gap by developing AI-based methods that learn to solve combinatorial optimization problems directly on temporal graphs.

This PhD project aims to explore the potential of machine learning methods as a means to efficiently solve combinatorial optimization problems on temporal graphs. We target three specific goals:

Goal 1: End-to-end learning framework.
We aim to design a framework that trains neural models to directly map problem instances to solutions in temporal graphs. While such approaches exist for static graphs, our challenge is to extend them to the temporal setting by defining suitable loss functions and training strategies.

Goal 2: A novel filter-based architecture.
We plan to develop a neural architecture that treats optimization as a filtering task — discarding irrelevant links to isolate the optimal subgraph. Building on spectral methods and recent work in temporal graph signal processing, we will explore how filters can be effectively defined and learned in a frequency-structure domain.

Goal 3: High-impact applications.
We will validate our methods on two key applications:

Anomaly localization: Many systems detect anomalies but fail to pinpoint their origin. We aim to learn to localize anomalies without relying on assumptions about their structure.

Temporal graph exploration: In transportation networks, finding optimal exploration routes is NP-hard. Our goal is to develop practical AI-based methods that scale better than current approximations.

The LISIC (Laboratoire d'Informatique Signal et Image de la Côte d’Opale) is a French research laboratory focused on computer science, signal processing, and artificial intelligence. Based in Calais and Saint-Omer, it brings together researchers working on topics such as machine learning, image and signal analysis, data science, and complex systems. LISIC is known for its interdisciplinary approach, combining theoretical advances with real-world applications, particularly in collaboration with local industries and institutions. The lab is part of the Université du Littoral Côte d’Opale (ULCO).

We look for highly motivated candidates with relevant experience in computer science, graph algorithms, and/or deep learning. Experience in Python programming and operations research will be a plus.

Starting date: October 2025
Duration: 3 years