About Me

I am full professor at Ecole Polytechnique in the Applied Mathematics Department, member of the CMAP: Center for Applied Mathematics, Inria team-leader of the project MΞDISIM (Mathematical and Mechanical Modeling with Data Interaction for Simulation in Medicine). I am also Ingénieur Général of The Corps des mines.

My main research concerns inverse problems, in particular identification problems or data assimilation problems in general for partial differential equation models, in which I seeking from designing and analyzing original methods. More precisely in the field of data assimilation approaches, my main investigation concerns observer-based methods from an optimal control point of view or from a stabilization point of view. I am also very concerned by the efficiency of the proposed methods so that they can be used in real applications in particular -- but not only -- in the design of digital twins for cardiovascular problem.

As my ambition is also to go up to the application, an important part of my researched is also devoted to modeling and the numerical aspects (computational methods and numerical analysis) of biomechanical systems such as the ones encountered in cardiac mechanics (non-linear mechanics, active soft tissue, fluid-structure interaction, poroelasticity, reaction-diffusion). My direction of research in modeling is to propose well-balanced formulations since they are a prerequisite for defining adequate stable observer when reconsidering them in the data assimilation context.

Selected publications from current research themes

• M. Doumic, P. Moireau. Asymptotic approaches in inverse problems for depolymerization estimation. Inverse Problems and Imaging, Published online 2025; 〈10.3934/ipi.2025020〉 〈hal-04713806/〉
• M. Boulakia, M. de Buhan, T. Delaunay, S. Imperiale, P. Moireau. Solving inverse source wave problem from Carleman estimates to observer design. Mathematical Control and Related Fields, Published online 2025; 〈10.3934/mcrf.2025007〉 〈hal-04788439v1/〉
• L.-P. Chaintron, F. Kimmig, M. Caruel, P. Moireau. A jump-diffusion stochastic formalism for muscle contraction models at multiple timescales, Journal of Applied Physics, 134, 194901 2023, 〈10.1063/5.0158191〉. 〈hal-04264293〉
• J. Manganotti, S. Imperiale, P. Moireau. Flow recovery from distal pressure in linearized hemodynamics: an optimal control approach. Inverse Problems, 39 (7), pp.075004. 2023; ,〈10.1088/1361-6420/acd274〉〈hal-04178851〉
• L.-P. Chaintron, A. M. González, L. Mertz, P. Moireau. Mortensen Observer for a class of variational inequalities - Lost equivalence with stochastic filtering approaches, ESAIM: Proceedings 73 2023; 〈hal-03659066〉
• M. Barré, C. Grandmont, and P. Moireau. Analysis of a linearized poromechanics model for incompressible and nearly incompressible materials. Evolution Equations and Control Theory 2022, 〈hal-03501526〉
• P. Moireau. Discrete-time formulations as time discretization strategies in data assimilation, Handbooks of Numerical Analysis, Numerical Control and beyond (B), chapter 7. Elseiver, 2023, 2023; 〈10.1016/bs.hna.2022.11.005〉 〈hal-03921465〉
• M. Aussal and P. Moireau. Kernel representation of Kalman observer and associated H-matrix based discretization. ESAIM : Control, Optimisation and Calculus of Variations, 28, 78 2022, 〈hal-03658937v1〉