2023-06295 - Post-Doctoral Research Visit F/M Inverse problems for nonlinear conservation laws and applications to cell physiology

Contract type : Fixed-term contract

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

Level of experience : Up to 3 years

About the research centre or Inria department

The Inria Saclay-Île-de-France Research Centre was established in 2008. It has developed as part of the Saclay site in partnership with Paris-Saclay University and with the Institut Polytechnique de Paris .

The centre has 39 project teams , 27 of which operate jointly with Paris-Saclay University and the Institut Polytechnique de Paris; Its activities occupy over 600 people, scientists and research and innovation support staff, including 44 different nationalities.

The centre also hosts the Institut DATAIA , dedicated to data sciences and their disciplinary and application interfaces.


Every year Inria International Relations Department has a few postdoctoral positions in order to support Inria international collaborations.
This year, postdoctoral positions within the frame of
Inria London, Inria Brasil and Inria Chile programs and to strengthen partnerships with Simula (Norway), University of Waterloo (Canada) and KAIST and ETRI (South Korea) are eligible.
The postdoc contract will have a duration of
12 to 24 months. The default start date is November 1st, 2023 and not later than January, 1st 2024. The postdoctoral fellow will be recruited by one of the Inria Centers in France but it is recommended that the time is shared between France and the partner’s country (please note that the postdoctoral fellow has to start his/her contract being in France and that the visits have to respect Inria rules for missions)


Candidates for postdoctoral positions are recruited after the end of their Ph.D. or after a first post-doctoral period: for the candidates who obtained their PhD in the Northern hemisphere, the date of the Ph.D. defense shall be later than 1 September 2021; in the Southern hemisphere, later than 1 April 2021.
In order to encourage mobility, the postdoctoral position must take place in a scientific environment that is truly different from the one of the Ph.D. (and, if applicable, from the position held since the Ph.D.); particular attention is thus paid to French or international candidates who obtained their doctorate abroad.

Main activities

This postdoctoral offer, co-supervized by Romain Yvinec (INRAE Tours / Inria Saclay) and Mauricio Sepúlveda (Universidad de Concepción), is within the framework of the associate team ANACONDA, whose focus is on the theoretical and numerical ANAlysis of CONservation laws for multicellular DynAmics. The consortium gather experts in mathematical biology, partial differental equations of conservation law type, and artificial intelligence, in order to bring new results in cell physiology. The recruited person will be in close connection with researchers of the ANACONDA associate team, and will spend part of her/his time in Chile.
The postdoctoral fellow will develop innovative inverse problems strategies, and apply them in a synergistic way to various cell biology processes studied in the team, including ovarian folliculogenesis maturation within the female reproductive system, cell-size dynamics in the adipocyte system, host-microbiota dialog at the intestinal crypt level. These applications share in common equations of conservation laws with non-local nonlinear terms whose inference with snapshot type data is challenging.
The research program includes (i) the study of the well-posedness of nonlinear non-local conservation laws developed in the team, and their associated adjoint formulations; (ii) the design of efficient numerical schemes for the direct and adjoint formulations; (iii) the resolution of the inverse problem on several test and application cases developed in the team. The latter will be based on two different approaches. A first one will consider optimization of a cost function thanks to gradient-based strategies derived from the adjoint formulation. This is a standard yet powerful approach, which has to be developed on a case by case study [1-4]. The second strategy will explore innovative physics-informed deep learning approaches, which take advantage of the underlying PDE system or its numerical scheme to construct the architecture of the neural networks that will learn model parameters [5-6].
With the help of the researchers in MUSCA, the post-doctoral fellow will finally tackle the identifiability issues and parameter value interpretation, in order to draw conclusions and predictions in the different physiological applications.

  1. D. Givoli, Dan, A tutorial on the adjoint method for inverse problems. Comput. Methods Appl. Mech. Engrg. 380 (2021),113810, 23 pp.
  2. A. Coronel, R. Lagos, P. Mulet, M. Sepúlveda, A numerical method for an inverse problem arising in two-phase fluid flow transport through a homogeneous porous medium. Numerical mathematics and advanced applications-ENUMATH, 2017, 615-623, Lect. Notes Comput. Sci. Eng., 126, Springer, Cham, 2019.
  3. R. Bürger, A. Coronel, M. Sepúlveda, Numerical solution of an inverse problem for a scalar conservation law modelling sedimentation. Hyperbolic problems: theory, numerics and applications, 445-454, Proc. Sympos. Appl. Math., 67, Part 2, Amer. Math. Soc., Providence, RI, 2009.
  4. A. Coronel, F. Huancas, M. Sepúlveda, Identification of space distributed coefficients in an indirectly transmitted diseases model. Inverse Problems 35 (2019), no. 11, 115001, 20 pp.
  5. Z. Cai, J. Chen, M. Liu, Least-squares neural network (LSNN) method for scalar nonlinear hyperbolic conservation laws: Discrete divergence operator, Journal of Comp. Appl. Maths., 2023, in press
  6. Z. Chen, A. Gelb, Y. Lee, Designing Neural Networks for Hyperbolic Conservation Laws, arXiv:2211.14375 2022



Technical skills and level required : A Ph.D in applied mathematics, with expert knowledge in PDEs and numerical analysis of PDEs.

Relational skills : Strong motivation to work in an interdisciplinary team.

Other valued appreciated : Experience in inverse problems and/or machine learning will be a plus

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


Monthly salary : 2.746 euros/month