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Table of Contents

Research topics 

- Numerical methods for kinetic and hyperbolic equations
- Scientific machine learning
- Micro-macro modeling in collective cell dynamics
- Applications in plasma physics

Current research projects

Supervision

PhD

  • Nicolas Pailliez (Oct. 2024-…, supervised with E. Franck, V. Michel-Dansac, S. Pamela). Représentation implicite neuronale et apprentissage d’opérateurs pour les problèmes multi-échelles en physique.
  • Claire Schnoebelen (Oct. 2023-…, supervised with E. Opshtein, E. Franck). Méthodes géométriques pour les problèmes d’ondes
  • Roxana Sublet (Oct. 2023-…, supervised with M. Szopos). Models for collective cell dynamics.
  • Yassin Rhalil (Oct. 2022-…, consultant, supervised by B. Famaey). Galactic potential reconstruction.
  • Guillaume Steimer (Oct. 2021-.., supervised with R. Côte, E. Franck, V. Vigon). Réduction de modèles par apprentissage profond pour la physique des plasmas
  • Léo Bois (Oct. 2020 - Dec. 2023, supervised with P. Helluy, E. Franck, V. Vigon). Méthodes numériques basées sur l’apprentissage pour les EDP hyperboliques et cinétiques [ tel-04314459v1]
  • Mickaël Bestard (Oct. 2020 - Dec. 2023, supervised with Y. Privat and E. Franck). Optimal control of nonlinear hyperbolic systems on networks: gradient-based and deep learning approaches [ tel-04327861v1]
  • Romane Hélie (Oct. 2019 - March 2023, supervised with P. Helluy, E. Franck). Relaxation scheme for the simulation of plasmas in tokamaks [ tel-04034510v2]
  • Pierre Gerhard (Oct. 2015 - Jan. 2020, supervised with P. Helluy and C. Foy). Réduction de modèles cinétiques et applications à l’acoustique du bâtiment [ tel-02445322v3]
  • Nhung Pham (Oct. 2012 - Dec. 2016, supervised with P. Helluy). Méthodes numériques pour l’équation de Vlasov réduite [ tel-01412750v2]

Post-doctoral

  • Leopold Trémant (Jan. 2023 - Aug. 2024, supervised with E. Franck, C. Courtès, M. Kraus), Geometric learning for ordinary differential equations.
  • Youssouf Nasseri, (Oct. 2022 - Sept. 2024, supervised with E. Franck, C. Courtès, V. Vigon), Reduced models for the Vlasov Fokker-Planck system using deep learning.
  • Ali Elarif (Jan. 2021 - Feb. 2022, supervised with M. Mehrenberger), Semi-Lagrangian methods for solutions with strong gradients.

Papers

Submitted

Reduced models and applications

  1. R. Côte, E. Franck, L. Navoret, V. Vigon, G. Steimer, Reduced order modeling using auto-encoder and Hamiltonian neural networks, Commun. in Comput. Phys., to appear, 2024. [ hal-04237799]

  2. C. Courtès, E. Franck, K. Lutz, L. Navoret, Y. Privat, Reduced modelling and optimal control of epidemiological individual‐based models with contact heterogeneity, Optimal Control Applications and Methods, 45(2), pp. 459-493, 2024. [ doi:10.1002/oca.2970][ hal-03664271]

  3. L. Bois, E. Franck, L. Navoret, V. Vigon, A neural network closure for the Euler-Poisson system based on kinetic simulations, Kinet. Relat. Models, 15(1), pp. 49-89, 2022. [ doi:10.3934/krm.2021044] [ hal-02965954]

Conference papers

  1. E. Franck, I. Lannabi, Y. Nasseri, L. Navoret, G. Parasiliti, G. Steimer, Hyperbolic reduced model for Vlasov-Poisson equation with Fokker-Planck collision, Esaim Proc., 2024. [ hal-04099697]

  2. S. Guisset, M. Gutnic, P. Helluy, M. Massaro, L. Navoret, N. Pham, M. Roberts, Lagrangian/Eulerian solvers and simulations for Vlasov-Poisson , ESAIM: Proc., 53, pp. 120-132. 2016. [ doi:10.1051/proc/201653008] [ hal-01239673]

  3. P. Helluy, L. Navoret, Nhung Pham, A. Crestetto, Reduced Vlasov-Maxwell simulations, Comptes Rendus Mécanique, 342(10-11):619–635, 2014. [ doi:10.1016/j.crme.2014.06.008] [ hal-00957045]

  4. P. Helluy, M. Massaro, L. Navoret, N. Pham, and T. Strub, Reduced Vlasov-Maxwell modeling, In PIERS Proceedings, Guangzhou, 2014, pages 2628–2632, 2014. [ hal-01097228]

  5. N. Pham, P. Helluy, L. Navoret, Hyperbolic approximation of the Fourier transformed Vlasov equation, In ESAIM: Proc., Congrés SMAI, Seignosse, 27-31 mai 2013, volume 45, pages 379–389. EDP Sciences, 2014. [ doi:10.1051/proc/201445039] [ hal-00872972]

Implicit schemes for multi-scale hyperbolic problems

  1. T. Bellotti, P. Helluy, L. Navoret, Fourth-order entropy-stable lattice Boltzmann schemes for hyperbolic systems, SIAM J. Sci. Comput., to appear, 2024. [ hal-04510582]

  2. N. Chaudhuri, L. Navoret, C. Perrin, E. Zatorska
    Hard congestion limit of the dissipative Aw-Rascle system
    Nonlinearity, 37, 2024.
    [ doi:10.1088/1361-6544/ad2b14] [ hal-03786853]

  3. M. Boileau, B. Bramas, E. Franck, R. Hélie, P. Helluy, L. Navoret
    Parallel kinetic scheme for transport equations in complex toroidal geometry
    The SMAI Journal of computational mathematics, 8, pp. 249-271, 2022.
    [ doi:10.3934/krm.2021044] [ hal-02404082v2]

  4. F. Bouchut, E. Franck, L.Navoret, A low cost semi-implicit low-Mach relaxation scheme for the full Euler equations, J. Scientific Comput., 83 (24), 2020. [ doi:10.1007/s10915-020-01206-z] [ hal-02420859]

  5. C. Courtès, D. Coulette, E. Franck, L. Navoret, Vectorial kinetic relaxation model with central velocity. Application to implicit relaxations schemes, Commun. in Comput. Phys., 27, pp. 976-1013, 2020. [ doi:10.4208/cicp.OA-2019-0013 ] [ hal-01942317v1]

  6. D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, L. Navoret. High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation, Computer and Fluids, 190, pp. 485-502, 2019. [ doi:10.1016/j.compfluid.2019.06.007 ] [ hal-0170661]

  7. P. Degond, P. Minakowski, L. Navoret, E. Zatorska, Finite volume approximations of the Euler system with variable congestion
    Computers and Fluids, 169, pp. 23–39, 2018. [ doi:10.1016/j.compfluid.2017.09.007] [ hal-01651479]

  8. P. Degond, J. Hua, L. Navoret, Numerical simulations of the Euler system with congestion constraint, J. Comp. Phys., 230(22), pp. 8057-8088, 2011. [ doi:10.1016/j.jcp.2011.07.010] [ hal-01651479v1]

Conference papers

  1. E. Franck, L. Navoret, Semi-implicit two-speed Well-Balanced relaxation scheme for Ripa model, FVCA, 2020. [ doi:10.1007/978-3-030-43651-3_70] [ hal-02407820]

  2. R. Hélie, P. Helluy, E. Franck, L. Navoret, Kinetic over-relaxation method for the convection equation with Fourier solver, FVCA, 2020. [ doi:10.1007/978-3-030-43651-3_71] [ hal-02427044]

  3. F. Drui, E. Franck, P. Helluy, L. Navoret, An analysis of over-relaxation in kinetic approximation, Comptes Rendus Mécanique, 347(3), 259-269, 2019. [ doi:10.1016/j.crme.2018.12.001] [ hal-01839092]

  4. D. Coulette, E. Franck, P. Helluy, M. Mehrenberger, L. Navoret, Palindromic discontinuous Galerkin method, FVCA 2017: Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, pp 171-178, 2017. [ doi:10.1007/978-3-319-57394-6_19] [ hal-01653049]

Numerical schemes for kinetic and hyperbolic problems

  1. L. Bois, E. Franck, L. Navoret, V. Vigon. Optimal control deep learning approach for viscosity design in DG schemes. J. Sci. Comput., to appear. [ hal-04213057]

  2. E. Franck, V. Michel-Dansac, L. Navoret, Approximately well-balanced Discontinuous Galerkin methods using bases enriched with Physics-Informed Neural Networks, J. Comp. Phys., 2024, [ hal-04246991v2]

  3. M. Bestard, E. Franck L. Navoret, Y. Privat, Optimal scenario for road evacuation in an urban environment, ZAMP, 2024. [ hal-04253010v1]

  4. M. Mehrenberger L Navoret, N. Pham, Recurrence phenomenon for Vlasov-Poisson simulations on regular finite element mesh, Commun. in Comput. Phys., 28, pp. 877-901, 2020. [ doi:10.4208/cicp.OA-2019-0022] [ hal-01942708]

  5. P. Degond, F. Deluzet, L. Navoret, A.-B. Sun, M.-H. Vignal. Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasi-neutrality, J. Comp. Phys., 229(16), pp. 5630-5652, 2010. [ doi:10.1016/j.jcp.2010.04.001] [ hal-00629561]

Conference papers

  1. M. Mehrenberger, L. Navoret, A.-T. Vu, Composition schemes for the guiding-center model, FVCA, 2023. [ doi:10.1007/978-3-031-40860-1_25] [ hal-04035921]

  2. M. Badsi, M. Mehrenberger, L. Navoret, Numerical stability of plasma sheath, ESAIM:Proc., 64, 17-36, 2018. [ doi:10.1051/proc/201864017] [ hal-01676656]

  3. M. Billaud Friess, B. Boutin, F. Caetano, G. Faccanoni, S. Kokh, F. Lagoutière, L. Navoret, A second order anti-diffusive Lagrange-Remap scheme for two-component flows, ESAIM: Proc., vol. 32, p. 149-162 (2011) doi:10.1051/proc/2011018 [ hal-00708605]

  4. F. Charles, N. Vauchelet, C. Besse, T. Goudon, I. Lacroix-Violet, J.-P. Dudon, L. Navoret, Numerical approximation of Knudsen layer for the Euler-Poisson system, ESAIM: Proc., vol. 32, p. 177-194 (2011). doi:10.1051/proc/2011018 [ hal-00708605]

  5. P. Degond, F. Deluzet, L. Navoret, An asymptotically stable Particle-in-Cell (PIC) scheme for collisionless plasma simulations near quasineutrality, C. R. Acad. Sci. Paris, Ser I, vol. 343, pp. 613-618 (2006). [ doi:10.1016/j.crma.2006.09.033]

Mathematical modelling of collective dynamics and applications in cell physics

  1. S. Lo Vecchio, O. Pertz, M. Szopos, L. Navoret, D. Riveline, Spontaneous rotations in epithelia as an interplay between cell polarity and RhoA activity at boundaries, Nature Physics, 20, pp. 322–331, 2024. [ doi:10.1038/s41567-023-02295-x] [ hal-03427805]

  2. S. Lo Vecchio, R. Thiagarajan, D.Caballero, V. Vigon, L. Navoret, R. Voituriez, D. Riveline, Cell motion as a stochastic process controlled by focal contacts dynamics, Cell Systems, 10(6), 2020.
    [ doi:10.1016/j.cels.2020.05.005] [ hal-02886195]

  3. B. Grec, B. Maury, N. Meunier, L. Navoret, A 1D model of leukocyte adhesion coupling bond dynamics with blood velocity, Journal of theoretical biology, 452, 35-46, 2018. [ doi:10.1016/10.1016/j.jtbi.2018.02.021] [ hal-01566770]

  4. P. Degond, L. Navoret, A multi-layer model for self-propelled disks interacting through alignment and volume exclusion, Math. Models Methods Appl. Sci., 25(13), 2439-2475, 2015. [ doi:10.1142/S021820251540014X ] [ hal-01118377]

  5. L. Navoret, A two-species hydrodynamic model of particles interacting through self-alignment, Math. Models Methods Appl. Sci., 23, pp. 1067, 2013. [ doi:10.1142/S0218202513500036] [ arXiv:1401.1379]

  6. S. Motsch, L. Navoret, Numerical simulation of a non-conservative hyperbolic problem with geometric constraints describing swarming behaviour, Multiscale Model. Simul., 9(3), pp. 1253-1275, 2011.
    [ doi:10.1137/100794067] [n arxiv:0910.2951]

  7. P. Degond, L. Navoret, R. Bon, D. Sanchez, Congestion in a macroscopic model of self-driven particles modeling gregariousness, J. Stat. Phys., vol. 138, pp. 85-125 (2010). [ doi:10.1007/s10955-009-9879-x ] [ hal-00409844]

Conference papers

  1. A. Cucchi, C. Etchegaray, N. Meunier, L. Navoret, L. Sabbagh, Cell migration in complex environments: chemotaxis and topographical obstacles,ESAIM: Proceedings and Surveys, 2020. [ doi:10.1051/proc/202067012] [ hal-02126709v2]

  2. C. Etchegaray, B. Grec, B. Maury, N. Meunier, L. Navoret, An integro-differential equation for 1D cell migration, Integral Methods in Science and Engineering (IMSE), 2014, Karlsruhe, Germany. Springer, pp.195-207, 2015, Integral Methods in Science and Engineering – Theoretical and Computational Advances. [ doi:10.1007/978-3-319-16727-5_17] [ hal-01083510]

  3. P. Degond, A. Frouvelle, J.-G. Liu,S. Motsch, L. Navoret, Macroscopic models of collective motion and self-organization, Séminaire Laurent Schwartz — EDP et applications (2012-2013), Exp. No. 1, 27 p. [ numdam:10.5802/slsedp.32]

  4. L. Navoret, R. Bon, P. Degond, J. Gautrais, D. Sanchez, G. Theraulaz
    Analogies between social interactions models and supply chains, ECMI 2008 Proceedings (2010) [ doi:10.1007/978-3-642-12110-4_84] [ hal-01872081v1]

Theses

  • L. Navoret, Models and numerical methods for multiscale transport problems, HDR Thesis, Université de Strasbourg, 2024 [ tel-04826632]

  • L. Navoret, Méthodes asymptotico-numériques pour des problèmes issus de la physique des plasmas et de la modélisation des interactions sociales, PhD Thesis, Université Toulouse - Paul Sabatier, 2010 [ tel-00568232]

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