Postdoctoral position : « Optimal control and numerical analysis for the Chemical Master Equation »

Post-Doctoral Research Visit F/M Optimal control and numerical analysis for the Chemical Master Equation

Date limite de candidature : 29/04/2023
Date de début : 01/09/2023
Date de fin : 01/09/2025

Pôle : Automatique et systèmes
Type de poste : Post-Doc ou ATER
Contact : Laurent Pfeiffer (

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 Post-Doctoral Research Visit F/M Optimal
control and numerical analysis for the Chemical Master

Type de contrat : CDD
Niveau de diplôme exigé : Thèse ou équivalent
Fonction : Post-Doctorant

A propos du centre ou de la direction fonctionnelle

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 34 project teams , 27 of which operate jointly with Paris-Saclay University (15 teams)
and the Institut Polytechnique de Paris (12 teams). 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.

Contexte et atouts du poste

The post-doc will take place within the framework of the OPT-MC project, acronym for « OPTimal
control of Markov Chains » and « OPTogenetics control of Microbial Communities ». The project is a
multidisciplinary project funded by the French National Agency for Research.

The project partners are

    . Laurent Pfeiffer (DISCO team)
    . Frédéric Bonnans (DISCO team)
    . Jakob Ruess (LIFEWARE team)

The team members have a long collaboration experience going back to theCOSY project.
The successful candidate will be mainly hosted within the DISCO team, affiliated to the Laboratory of
Signals and Systems of CentraleSupélec. Travel expenses for regular conference participations will be
covered by the project.

Mission confiée

Scientific context

The Chemical Master Equation (CME) is a linear differential system which describes the progres of a
set of chemical reactions. When only a low number of molecules is involved, the occurence of
chemical reactions is inherently stochastic and can be modeled with a continuous-time Markov chain
(CTMC) [1].

The CME is particularly well-suited to describe a population of cells inside which biochemical
processes occur, shaping the functionality of the cells. These processes being stochastic, two
genetically identical cells can take different configurations: this phenomenon is call cell-to-cell
variability (or heterogeneity); it is pervasive in biology and cannot be neglected. OFen the cell
population is subject to other mechanisms such as cellular growth or selection. The CME framework
can be extended in order to take into account these mechanisms [5].

We are interested in the optimal control of cell populations: exposing the cells to a light-stimulus of
variable intensity, we can control the reactions rates of biochemical processes leading to the
production (to be maximized) of some proteins of interest.

Main objectives

The postdoc will work on the mathematical analysis of the CME (and its PDE-approximations) and on
the development of numerical methods for the simulation and the optimization of the CME.

Principales activités

Mathematical aspects

The investigation of the CME, as a mathematical object is a difficult task, as the state space is
infinite (yet countable) and the transition rates of the underlying CTMC are unbounded and
time-dependent (when controlled through an optical device). We aim at developping a
mathematical framework for the rigorous investigation of the CME and its extensions,
covering the largest possible range of applications, and extending the classical analysis of
forward equations for CTMCs [2].

At a numerical level, the simulation and the approximation of the CME is in general a
challenging task, the number of states to consider being usually very large (it increases
exponentially with the number of reactants). We have a special interest in the Kramers-
Moyal approximation (and more generally in continuum approximations [4] consisting in
approximating the CME with a Fokker-Planck equation (including non-local terms in the
extended framework [5]). The theoretical investigation of the reesulting Fokker-Planck
equation and the quality of the Kramers-Moyal approximation are topics of interest, beyond
applications in biology.

Finally, we aim at developping complete optimization procedures for the CME and its
approximations, leveraging various standard techniques from optimal control theory [3],
related to singular arcs or the turnpike phenomenon, for example.


1. Anderson and Kurtz. Continuous time markov chain models for chemical reaction networks.
In Design and analysis of biomolecular circuits: engineering approaches to systems and
synthetic biology. Springer, 2011. [link]
2. Anderson. Continuous-time Markov chains: An applications-oriented approach. Springer, 1991. [link]
3. Caillau, Ferretti, Trélat, and Zidani. Numerics for finite-dimensional optimal control
problems. 2022. [link]
4. Lunz. On continuum approximations of discrete-state markov processes of large system
size. Multiscale Modeling & Simulation, 2021. [link]
5. Lunz, Batt, Ruess, and Bonnans. Beyond the chemical master equation: stochastic chemical
kinetics coupled with auxiliary processes. PLoS Computational Biology, 2021. [link]


Candidates should have a PhD in mathematics or control engineering. Experience with either
optimization theory, PDEs or with stochastic processes is expected. Good programming skills are

Scientific expertise in biology is not required but candidates are expected to build up an
understanding of our concrete applications throughout the course of the project.


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 (aFer 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

2746 €/month (gross salary)