PhD Position "Interactions between microscopic and macroscopic models for autonomous vehicles in human-driven environments"

May 28, 2023
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2023-05891 - PhD Position "Interactions between microscopic and macroscopic models for autonomous vehicles in human-driven environments"

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : Tempary Research Position

About the research centre or Inria department

The Inria Université Côte d'Azur center counts 37 research teams as well as 8 support services. The center's staff (about 500 people) is made up of scientists of different nationalities, engineers, technicians and administrative staff. The majority of the center's research teams are located in Sophia Antipolis and five of them are based in an Inria antenna in Montpellier. The Inria branch in Montpellier is growing in size, in accordance with the strategy described in the institution's Contract of Objectives and Performance (COP).


DATAHYKING MSCA Joint Doctorates Network (https:// aims at training a new generation of modeling and simulation experts to develop virtual experimentation tools and workflows that can reliably and efficiently exploit the potential of mathematical modeling and simulation of interacting particle systems.

To this end, DATAHYKING unites researchers from 7 research institutes (KU Leuven, Università degli Studi di Ferrara, Università di Roma Sapienza, RWTH Aachen, Technische Universität Kaiserslautern, Université de Lille and INRIAi). This consortium will create a data-driven simulation framework for kinetic and hyperbolic models of interacting particle systems and define a common methodology for these future modeling and simulation experts. DATAHYKING will focus on:

  • Developing reliable and efficient simulation methods;
  • Designing robust consensus-based optimization , also for machine learning;
  • Developing multifidelity methods for uncertainty quantification and data assimilation ;
  • Applications in traffic flow, finance, and granular flow, also in collaboration with industry.
  • We offer a fully funded 3-year joint PhD position between Inria Centre of Université Côte d'Azur and Università di Roma La Sapienza. The successful candidate will spend the first 18 months of this PhD at Inria (Sophia Antipolis, France), the next 18 months at La Sapienza (Roma, Italy). A 6-month secondment to Autovie Venete (Palmanova, Italy) is foreseen to work on an industrial case study.

    ACUMES Project-Team (https://, leaded by Paola Goatin (https://, is a joint team from Inria Centre of Université Côte d'Azur and the Mathematics department Jean-Alexandre Dieudonné (LJAD) of Nice University. The research conducted concerns the analysis and optimization of systems governed by partial differential equations, with applications ranging from fluid and structural mechanics to modeling of biological phenomena, road and pedestrian traffic. In particular, ACUMES Project-Team has an established experience in (macroscopic) traffic flow modeling, simulation and optimization, including industrial and international collaboration.

    The Department of Mathematics Guido Castelnuovo at University of Rome "La Sapienza" is one of the most important in Italy and takes a prominent place in the history of mathematics. The excellence of the research performed, together with the wide-ranging collaborative relationships maintained by researchers in the Department of Mathematics, guarantee the high quality of the doctoral program. In particular, the research group in numerical analysis gathers, among others, experts in multiscale mathematical modeling and high order finite volume schemes for conservation laws.


  • High-level and exciting international research environment
  • Supportive and collaborative team for developing know-how and expertise in state-of-the-art simulation methods
  • Opportunity to build up research and innovation skills that are essential for a future career in research and development, both in an industrial and academic context
  • Competitive salary
  • Assignment

    During the first phase at Inria, the PhD student will study micro-macro models consisting of coupled PDE-ODE systems to describe the mutual interaction between a finite number of particles and a fluid flow and allow designing efficient control strategies to regulate traffic flow by acting on the speed of a few controlled vehicles. She/he will develop new PDE-ODE coupled multilane models for the mutual interactions between the main (human-driven) flow and a small number of specific autonomous particles/agents. We will study the well-posedness of the resulting systems, develop numerical schemes to compute approximate solutions and study the dependence of model properties of interest on particle penetration rate.

    The second phase at La Sapienza will be devoted to the development of mixture models, containing human-driven and a small percentage of autonomous cars. These models result in macroscopic flow models, coupled with ODEs for driver behavior. She/he will develop efficient numerical methods for these models and study the sensitivity of the stability of traffic flow with respect to the interaction rules at the microscopic level between autonomous and human driven cars, as well as the effect of partially autonomous cars with increasing levels of automation.

    The secondment at Autovie Venete will focus on model calibration against real world data provided by the industrial partner.

    Main activities

    After a complete literature review, the research fellow will develop and investigate multi-scale traffic flow models, including the well-posedness and other analytical properties and the development and coding of specific numerical schemes. She/he will also validate the results against real traffic data.

    Writing reports and journal and conference papers on the results.

    Present and communicate the results at workshops, conferences, etc.


    Technical skills and level required : experienced knowledge of Matlab (alternatively Python), Latex (bibtex, tikz, beamer).

    Languages : English level B2

    Relational skills : good communication and team skills

    Please send also an email [email protected] to announce your application.

    Benefits package
  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage
  • General Information
  • Theme/Domain : Numerical schemes and simulations Scientific computing (BAP E)

  • Town/city : Sophia Antipolis

  • Inria Center : Centre Inria d'Université Côte d'Azur
  • Starting date : 2023-09-01
  • Duration of contract : 1 year, 6 months
  • Deadline to apply : 2023-05-28
  • Contacts
  • Inria Team : ACUMES
  • Recruiter : Goatin Paola / [email protected]
  • The keys to success
  • Master degree in mathematics, mathematical engineering or equivalent
  • Scientific background in Partial Differential Equations (PDE) analysis, numerical analysis and computer simulations.
  • Knowledge of hyperbolic systems of conservation laws and finite volume schemes, statistics, data analysis as well as experience in mathematical modelling and/or optimization techniques are considered an additional plus.
  • An organized, independent work ethic
  • About Inria

    Inria is the French national research institute dedicated to digital science and technology. It employs 2,600 people. Its 200 agile project teams, generally run jointly with academic partners, include more than 3,500 scientists and engineers working to meet the challenges of digital technology, often at the interface with other disciplines. The Institute also employs numerous talents in over forty different professions. 900 research support staff contribute to the preparation and development of scientific and entrepreneurial projects that have a worldwide impact.

    Instruction to apply

    Candidates should comply with MCSA mobility rules: they must not have resided or carried out their main activity (work, studies, etc.) in the country of the recruiting organisation for more than 12 months in the 36 months immediately before their recruitment date

    Defence Security : This position is likely to be situated in a restricted area (ZRR), as defined in Decree No. 2011-1425 relating to the protection of national scientific and technical potential (PPST).Authorisation to enter an area is granted by the director of the unit, following a favourable Ministerial decision, as defined in the decree of 3 July 2012 relating to the PPST. An unfavourable Ministerial decision in respect of a position situated in a ZRR would result in the cancellation of the appointment.

    Recruitment Policy : As part of its diversity policy, all Inria positions are accessible to people with disabilities.

    Warning : you must enter your e-mail address in order to save your application to Inria. Applications must be submitted online on the Inria website. Processing of applications sent from other channels is not guaranteed.

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