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MSCA-COFUND-CLEAR-Doc-PhD Position#CD22-44: Formal verification of neural ODE for safety evaluation in autonomous vehicles


Job Information

Université Gustave Eiffel
Research Field
Engineering » Control engineering
Computer science
Researcher Profile
First Stage Researcher (R1)
Application Deadline
Type of Contract
Job Status
Hours Per Week
Is the job funded through the EU Research Framework Programme?
H2020 / Marie Skłodowska-Curie Actions COFUND
Marie Curie Grant Agreement Number
Is the Job related to staff position within a Research Infrastructure?

Offer Description


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.


Research Field
Education Level
Bachelor Degree or equivalent
Research Field
Computer science
Education Level
Bachelor Degree or equivalent
  • At the time of the deadline, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree.
  • At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle to embark on a doctorate.
Specific Requirements

The position should interest candidates who hold a Master’s degree in automatic control (preferred), computer science, artificial intelligence or related fields.

A specialization or experience in one or more of the following areas will be appreciated:

  • control engineering, experience with ordinary differential equations,
  • artificial intelligence, machine learning, neural networks,
  • formal methods,
  • dependability techniques.

A good level in English is also required.


Additional Information

  • High-quality doctoral training rewarded by a PhD degree, delivered by Université Gustave Eiffel
  • Access to cutting-edge infrastructures for research & innovation.
  • Appointment for a period of 36 months based on a salary of 2 700 € (gross salary per month).
  • Job contract under the French labour legislation in force, respecting health and safety, and social security: 35 hours per week contract, 25 days of annual leave per year.
  • International mobility will be mandatory
  • An international environment supported by the adherence to the European Charter & Code.
  • Access to dedicated CLEAR-Doc trainings with a strong interdisciplinary focus, together with a Career development Plan.
Eligibility criteria

Applicants must fulfil the following eligibility criteria:

  • At the time of the deadline, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree.
  • At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle to embark on a doctorate.
  • At the time of the deadline, applicants must be in the first four years (full-time equivalent research experience) of their research career (career breaks excluded) and not yet been awarded a doctoral degree. Career breaks refer to periods of time where the candidate was not active in research, regardless of his/her employment status (sick leave, maternity leave etc). Short stays such as holidays and/or compulsory national service are not taken into account.
  • At the time of the deadline, applicants must fulfil the transnational mobility rule: incoming applicants must not have resided or carried out their main activity (work, studies, etc.) in France for more than 12 months in the 3 previous years.
  • One application per call per year is allowed.
  • Applicants must be available full-time to start the programme on schedule (November 1st 2023).
  • Application rules are enforced by the French doctoral system which specifies a standard duration of 3 years for a full-time PhD together with the MSCA standards and the OTM-R European rules as follows.
  • Citizens of any nationality may apply to the programme.
  • There is no age limit.
Selection process

Please refer to the Guide for Applicants available on the CLEAR-Doc website:

Additional comments
  • The First step before applying is contacting the PhD supervisor. You will not be able to apply without an acceptation letter from the PhD supervisor.
  • International mobility planned:

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.

  • Please contact the PhD supervisor for any additional detail on job offer.
  • There are no restrictions concerning the age, gender or nationality of the candidates. Applicants with career breaks or variations in the chronological sequence of their career, with mobility experience or with interdisciplinary background or private sector experience are welcome to apply.
  • Support service is available during every step of the application process by email:
Website for additional job details

Work Location(s)

Number of offers available
Université Gustave Eiffel
Villeneuve-d Ascq
Postal Code
20 Rue Élisée Reclus


Marne la Vallée
5, Boulevard Descartes
Postal Code