*Context*

Université Gustave Eiffel is a multi-campus national university in France which was born in 2020 out of the merger of Université Paris-Est Marne-la-Vallée and IFSTTAR, the Institute for European Research on Cities and Regions, Transport and Civil Engineering. It includes a school of architecture, EAV&T, and three engineering schools, EIVP, ENSG Géomatique and ESIEE Paris. By creating for the first time in France a three-way partnership between a university, research organisations and schools of architecture and engineering , it will have the specific purpose of fostering national and international partnerships to meet the major societal challenges generated by the profound changes in urban areas, which are already home to 55% of mankind.

The COSYS ("Components and Systems") department aims to develop the necessary concepts and tools for improving basic knowledge, methods, technologies and operational systems intended for a renewed intelligence of mobility, networks infrastructure and major urban systems. It therefore aims to gain greater control over their efficiency, their safety, their carbon footprint and their impact on the environment and health. The production of knowledge at the frontier of practices, their transformation into useful products and into a doctrine set as a support to public policies and the evaluation of the transformations induced by innovations in these fields of activity, form the DNA of the department.

The ESTAS laboratory "Evaluation and Safety of Automated Transport Systems" develops methods, techniques and tools intended to facilitate and improve the analysis and assessment of the safety functions of guided transport systems. The finalized research, which is one of the main features of ESTAS, finds its foundations in the synergy between applied research and feedback from expertise and technical assistance activities in the field of guided transport systems. This kind of applied research operates on a specific way that heavily relies on the needs raised by the expertise and technical assistance activities, to respond to practical concerns of the field.

*Topic description*

A higher autonomy is an increasingly common goal in the design of the transportation systems for the cities of tomorrow. Recently, part of this autonomy in both road and rail transportation has come from the field of artificial intelligence and machine learning, particularly for perception tasks (detection and recognition of road signs, rail signals, or other elements of the vehicle’s environment) using neural networks. While AI-based approaches have gained significant popularity in many application fields due to their good performances, their unpredictability and absence of formal guarantees regarding their desired behavior present a major issue for the deployment of safety-critical systems such as autonomous vehicles in urban areas. The goal of this PhD thesis is thus to design new formal methods to analyse and ensure the safety of such AI-based perception modules in autonomous vehicles.

More specifically, this PhD topic aims to formally evaluate the safety of a recently introduced class of AI models: neural ordinary differential equations (neural ODE). Unlike the classically used neural networks which are modeled as discrete graphs with a finite number of layers and neurons, neural ODE are modeled as ordinary differential equations which can be seen as a continuous extension of neural networks. Neural ODE have already been used successfully for image recognition tasks showing higher performances compared to classical neural networks, but current works in the literature primarily focus on their training performances, while they have been barely studied in terms of safety and formal guarantees.

The main scientific challenges that will be considered during this PhD work are the following:

- Definition and analysis of new types of continuous generalization of neural networks into neural ODE. Comparison of their performances with respect to the discrete neural networks.

- Analysis of the mathematical properties satisfied by the new continuous models (continuity, monotonicity, contraction, stability, ...)

- Exploiting these mathematical properties to study and/or enforce the overall behavior of the neural ODE with respect to various features: stability, stabilization, reachability analysis, safety, formal verification.

- Establishing formal relations between the discrete and continuous neural models, and using them to deduce the safety of one model based on the safety verification of the other.

Different applications will be targeted within this work. Current works at the ESTAS laboratory already consider the development of safety analysis approaches of AI modules within autonomous trains and road shuttles. The Department of Marine Technology of NTNU (Trondheim, Norway), hosting the 6-month international mobility of this PhD program, is also interested in problems of safe mobility but with a focus on maritime systems, including autonomous underwater vehicles, autonomous urban ferries to be used as public shuttles over the river crossing the city of Trondheim, and using AI to estimate the environment of a ship.

The above scientific challenges will thus be developed while targeting these application fields of interest for both ESTAS and NTNU, with more specific tasks including: detection and recognition of rail signals, road signs, obstacles, pedestrians and other users and objects surrounding the rail, road or water autonomous vehicles.

International mobility:

During this 3-year PhD program, a 6-month international mobility is planned in the Department of Marine Technology of NTNU (Norwegian University of Science and Technology) in Trondheim, Norway. More specifically, the student will be supervised during this mobility by Associate Professor Astrid H. Brodtkorb in the Marine Control group.

The Marine Control group works on many aspects related to control for ships, underwater vehicles and ocean structures. One of our core activities includes developing enabling technologies for safe autonomous operation of ships, where autonomous urban water transport is one case study. Topics include situational awareness, artificial intelligence, risk-based control architecture, simulation-based testing, and correct-by-design control algorithms. The activity on autonomous marine operations is multidisciplinary, with close collaboration with the Marine Risk group and the Department of Engineering Cybernetics through projects like SFI AutoShip, ORCAS and UNLOCK.

Similarly to many other application domains, the Marine Control group has recently taken an interest in the use of artificial intelligence modules in marine and maritime applications. This includes docking of automated underwater and surface vehicles, camera vision, and estimating the environment (sea state, current, ice, wind predictions).

This 6-month mobility at NTNU will be planned during the second year or start of the third year of the PhD program (between late 2024 and early 2026). It will give the opportunity for the student to interact with a team strongly focused on a different application domain, but still related to the core topics of this PhD: safe mobility and transportation systems. In addition to applying to marine applications the formal verification methods developed during the first two years of the PhD, the student will also benefit from a rich environment with possible interactions and collaborations with:

- the Marine Risk group lead by Professor Ingrid Utne, working broadly on safety and risk assessment in marine applications;

- the group of Professor Ekaterina Kim, using artificial intelligence to capture details of ice conditions around a ship;

- the Department of Engineering Cybernetics, where several researchers work on topics related to autonomous ships, for instance through the SFI AutoShip project for the development of autonomous passenger ferries for urban water transport.