PhD Position "Modeling and optimization of multi-modal transportation networks based on kinetic and hyperbolic equations"

2023-05896 - PhD Position "Modeling and optimization of multi-modal transportation networks based on kinetic and hyperbolic equations"

Contract type : Fixed-term contract

Level of qualifications required : Graduate degree or equivalent

Fonction : Tempary Research Position

Context

DATAHYKING MSCA Joint Doctorates Network (https:// datahyking.eu/) 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 Technische Universität Kaiserslautern. The successful candidate will spend the first 18 months of this PhD at Inria (Sophia Antipolis, France), the next 18 months at TUK (Kaiserslautern, Germany). A 6-month secondment at Transport and Mobility Leuven (Leuven, Belgium) is foreseen to work on an industrial case study.

ACUMES Project-Team (https:// team.inria.fr/acumes), leaded by Paola Goatin (https:// www-sop.inria.fr/members/Paola.Goatin/index.html), 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.

AGTM Project-Team (https: // www. mathematik.uni-kl.de/techno) led by Axel Klar (https: // www. mathematik.uni-kl.de/techno/personen/leitung/prof-dr-axel- klar), is a research unit at the department of mathematics of RPTU Kaiserslautern. AGTM works in the areas of modeling, analysis, numerics and optimization of partial differential equations related to problems from science, engineering and industry. This includes mathematical analysis of the equations, as well as development and analysis of numerical algorithms, and software implementation for real world problems in science and engineering. Current research topics are multiscale simulation, modelling and simulation of network structures, moment methods in kinetic theory, uncertainty quantification, optimization and control. Current applications include nano- technology, traffic flow modelling, bio-medical applications and material science.

Highlights:

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

Kinetic and hyperbolic traffic models are widely used to describe and simulate vehicular flows on networks, including multi-class traffic with different mobility modes (cars, buses, tramways, bicycles, etc.) on the same network.

During the first phase at Inria, the research fellow will design multi-class models on road networks (including dynamics at nodes for different transportation modes), develop corresponding finite volume numerical schemes, and design and implement selfish and cooperative routing strategies. She/he will analyze equilibria and design optimal control strategies to improve network throughput.

The second phase at TUK will be devoted to the development of suitable and efficient numerical methods to simulate and optimize the complex interactions between different classes of traffic modes and the corresponding coupling conditions on networks.

The secondment at Transport and Mobility Leuven will focus on the integration of multiclasssimulation tools in the industrial partner's workflow.

Main activities

After a complete literature review, the research fellow will develop and investigate multi-class traffic flow models on networks, including the development and coding of specific numerical schemes and the implementation of optimization strategies. 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.

Skills

Technical skills and level required : experienced knowledge of Matlab (alternatively Pyton), 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 : 2023-04-23

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

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.