Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
XML PDF e-pub
PDF e-Pub


Bibliography

Major publications by the team in recent years
[1]
A. Aggarwal, R. M. Colombo, P. Goatin.
Nonlocal systems of conservation laws in several space dimensions, in: SIAM Journal on Numerical Analysis, 2015, vol. 52, no 2, pp. 963-983.
https://hal.inria.fr/hal-01016784
[2]
L. Almeida, P. Bagnerini, A. Habbal, S. Noselli, F. Serman.
A Mathematical Model for Dorsal Closure, in: Journal of Theoretical Biology, January 2011, vol. 268, no 1, pp. 105-119. [ DOI : 10.1016/j.jtbi.2010.09.029 ]
http://hal.inria.fr/inria-00544350/en
[3]
B. Andreianov, P. Goatin, N. Seguin.
Finite volume schemes for locally constrained conservation laws, in: Numer. Math., 2010, vol. 115, no 4, pp. 609–645, With supplementary material available online.
[4]
S. Blandin, P. Goatin.
Well-posedness of a conservation law with non-local flux arising in traffic flow modeling, in: Numerische Mathematik, 2015. [ DOI : 10.1007/s00211-015-0717-6 ]
https://hal.inria.fr/hal-00954527
[5]
R. M. Colombo, P. Goatin.
A well posed conservation law with a variable unilateral constraint, in: J. Differential Equations, 2007, vol. 234, no 2, pp. 654–675.
[6]
M. L. Delle Monache, P. Goatin.
Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result, in: J. Differential Equations, 2014, vol. 257, no 11, pp. 4015–4029.
[7]
M. L. Delle Monache, J. Reilly, S. Samaranayake, W. Krichene, P. Goatin, A. Bayen.
A PDE-ODE model for a junction with ramp buffer, in: SIAM J. Appl. Math., 2014, vol. 74, no 1, pp. 22–39.
[8]
R. Duvigneau, P. Chandrashekar.
Kriging-based optimization applied to flow control, in: Int. J. for Numerical Methods in Fluids, 2012, vol. 69, no 11, pp. 1701-1714.
[9]
A. Habbal, M. Kallel.
Neumann-Dirichlet Nash strategies for the solution of elliptic Cauchy problems, in: SIAM J. Control Optim., 2013, vol. 51, no 5, pp. 4066–4083.
[10]
M. Kallel, R. Aboulaich, A. Habbal, M. Moakher.
A Nash-game approach to joint image restoration and segmentation, in: Appl. Math. Model., 2014, vol. 38, no 11-12, pp. 3038–3053.
http://dx.doi.org/10.1016/j.apm.2013.11.034
[11]
M. Martinelli, R. Duvigneau.
On the use of second-order derivative and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics, in: Computers and Fluids, 2010, vol. 37, no 6.
[12]
S. Roy, A. Borzì, A. Habbal.
Pedestrian motion modelled by Fokker–Planck Nash games, in: Royal Society open science, 2017, vol. 4, no 9, 170648 p.
[13]
M. Twarogowska, P. Goatin, R. Duvigneau.
Macroscopic modeling and simulations of room evacuation, in: Appl. Math. Model., 2014, vol. 38, no 24, pp. 5781–5795.
[14]
G. Xu, B. Mourrain, A. Galligo, R. Duvigneau.
Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method, in: J. Comput. Physics, November 2013, vol. 252.
[15]
B. Yahyaoui, M. Ayadi, A. Habbal.
Fisher-KPP with time dependent diffusion is able to model cell-sheet activated and inhibited wound closure, in: Mathematical biosciences, 2017, vol. 292, pp. 36–45.
Publications of the year

Doctoral Dissertations and Habilitation Theses

[16]
K. Chahour.
Modeling coronary blood flow using a non newtonian fluid model : fractional flow reserve estimation, Université Nice Sophia Antipolis, December 2019.
https://hal.inria.fr/tel-02430901

Articles in International Peer-Reviewed Journals

[17]
F. Berthelin, P. Goatin.
Regularity results for the solutions of a non-local model of traffic, in: Discrete and Continuous Dynamical Systems - Series A, 2019, vol. 39, no 6, pp. 3197-3213.
https://hal.archives-ouvertes.fr/hal-01813760
[18]
E. Bertino, R. Duvigneau, P. Goatin.
Uncertainty quantification in a macroscopic traffic flow model calibrated on GPS data, in: Mathematical Biosciences and Engineering, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-02379540
[19]
K. Chahour, R. Aboulaich, A. Habbal, N. Zemzemi, C. Abdelkhirane.
Virtual FFR quantified with a generalized flow model using Windkessel boundary conditions ; Application to a patient-specific coronary tree, in: Computational and Mathematical Methods in Medicine, 2020, forthcoming.
https://hal.inria.fr/hal-02427411
[20]
R. Chamekh, A. Habbal, M. Kallel, N. Zemzemi.
A nash game algorithm for the solution of coupled conductivity identification and data completion in cardiac electrophysiology, in: Mathematical Modelling of Natural Phenomena, February 2019, vol. 14, no 2, 15 p, forthcoming. [ DOI : 10.1051/mmnp/2018059 ]
https://hal.archives-ouvertes.fr/hal-01923819
[21]
F. A. Chiarello, J. Friedrich, P. Goatin, S. Göttlich, O. Kolb.
A non-local traffic flow model for 1-to-1 junctions, in: European Journal of Applied Mathematics, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-02142345
[22]
F. A. Chiarello, P. Goatin.
Non-local multi-class traffic flow models, in: Networks and Heterogeneous Media, 2019.
https://hal.archives-ouvertes.fr/hal-01853260
[23]
F. A. Chiarello, P. Goatin, E. Rossi.
Stability estimates for non-local scalar conservation laws, in: Nonlinear Analysis: Real World Applications, 2019, vol. 45, pp. 668-687, https://arxiv.org/abs/1801.05587. [ DOI : 10.1016/j.nonrwa.2018.07.027 ]
https://hal.inria.fr/hal-01685806
[24]
F. A. Chiarello, P. Goatin, L. M. Villada.
Lagrangian-Antidiffusive Remap schemes for non-local multi-class traffic flow models, in: Computational and Applied Mathematics, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-01952378
[25]
M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, M. S. Mohamed, P. Genevet.
Global optimization of metasurface designs using statistical learning methods, in: Scientific Reports, November 2019, vol. 9, no 1. [ DOI : 10.1038/s41598-019-53878-9 ]
https://hal.archives-ouvertes.fr/hal-02156881
[26]
C. Fiorini, C. Chalons, R. Duvigneau.
A modified sensitivity equation method for the Euler equations in presence of shocks, in: Numerical Methods for Partial Differential Equations, 2019, forthcoming.
https://hal.inria.fr/hal-01817815
[27]
P. Goatin, N. Laurent-Brouty.
The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model, in: Zeitschrift für Angewandte Mathematik und Physik, January 2019, vol. 70, no 31. [ DOI : 10.1007/s00033-018-1071-1 ]
https://hal.inria.fr/hal-01760930
[28]
P. Goatin, E. Rossi.
A multi-lane macroscopic traffic flow model for simple networks, in: SIAM Journal on Applied Mathematics, 2019, vol. 79, no 5, https://arxiv.org/abs/1904.04535. [ DOI : 10.1137/19M1254386 ]
https://hal.inria.fr/hal-02092690
[29]
P. Goatin, E. Rossi.
Well-posedness of IBVP for 1D scalar non-local conservation laws, in: Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2019, vol. 99, no 11, https://arxiv.org/abs/1811.09044. [ DOI : 10.1002/zamm.201800318 ]
https://hal.inria.fr/hal-01929196
[30]
A. Habbal, M. Kallel, M. Ouni.
Nash strategies for the inverse inclusion Cauchy-Stokes problem, in: Inverse Problems and Imaging , 2019, vol. 13, no 4, 36 p. [ DOI : 10.3934/ipi.2019038 ]
https://hal.inria.fr/hal-01945094
[31]
E. Rossi, J. Kötz, P. Goatin, S. Göttlich.
Well-posedness of a non-local model for material flow on conveyor belts, in: ESAIM: Mathematical Modelling and Numerical Analysis, 2019, https://arxiv.org/abs/1902.06488 - MSC: 35L65, 65M12, forthcoming. [ DOI : 10.1051/m2an/2019062 ]
https://hal.inria.fr/hal-02022654
[32]
E. Rossi.
Well-posedness of general 1D Initial Boundary Value Problems for scalar balance laws, in: Discrete and Continuous Dynamical Systems - Series A, 2019, vol. 39, no 6, pp. 3577-3608, https://arxiv.org/abs/1809.06066. [ DOI : 10.3934/dcds.2019147 ]
https://hal.inria.fr/hal-01875159
[33]
T. Zineb, R. Ellaia, A. Habbal.
New hybrid algorithm based on nonmonotone spectral gradient and simultaneous perturbation, in: International Journal of Mathematical Modelling and Numerical Optimisation, 2019, vol. 9, no 1, pp. 1-23. [ DOI : 10.1504/IJMMNO.2019.096911 ]
https://hal.inria.fr/hal-01944548

International Conferences with Proceedings

[34]
A. Festa, P. Goatin.
Modeling the impact of on-line navigation devices in traffic flows, in: CDC 2019 - 58th IEEE Conference on Decision and Control, Nice, France, IEEE Conference on Decision and Control, December 2019.
https://hal.archives-ouvertes.fr/hal-02379576
[35]
S.-X. Tang, A. Keimer, P. Goatin, A. Bayen.
A study on minimum time regulation of a bounded congested road with upstream flow control, in: CDC 2019 - 58th IEEE Conference on Decision and Control, Nice, France, IEEE Conference on Decision and Control, December 2019.
https://hal.archives-ouvertes.fr/hal-02379589

Conferences without Proceedings

[36]
R. Duvigneau.
Adaptive Refinement for Compressible Flow Analysis using an Isogeometric Discontinuous Galerkin Method, in: IGA 2019 - 7th International Conference on Isogeometric Analysis, Munich, Germany, September 2019.
https://hal.inria.fr/hal-02313641
[37]
R. Duvigneau, S. Pezzano, M. Stauffert.
A NURBS-based Discontinuous Galerkin method for CAD compliant flow simulations, in: SHARK-FV 2019 - Conference on Sharing Higher-order Advanced Research Know-how on Finite Volume, Minho, Portugal, May 2019.
https://hal.inria.fr/hal-02303621
[38]
M. M. R. Elsawy, S. Lanteri, R. Duvigneau, G. Brière, P. Genevet.
Optimized 3D metasurface for maximum light deflection at visible range, in: META 2019 - 10th International Conference on Metamaterials, Photonic Crystals and Plasmonics, Lisbonne, Portugal, July 2019, vol. 2019.
https://www.hal.inserm.fr/inserm-02430395
[39]
S. Pezzano, R. Duvigneau.
An Arbitrary Lagrangian Eulerian Formulation for Isogeometric Discontinuous Galerkin Schemes, in: IGA 2019 - 7th International Conference on Isogeometric Analysis, Munich, Germany, September 2019.
https://hal.inria.fr/hal-02313649
[40]
M. Stauffert, R. Duvigneau.
Shape Sensitivity Analysis for Hyperbolic Systems using an Isogeometric Discontinuous Galerkin Method, in: IGA 2019 - 7th International Conference on Isogeometric Analysis, Munich, Germany, September 2019.
https://hal.inria.fr/hal-02313657

Internal Reports

[41]
J.-A. Desideri.
Platform for prioritized multi-objective optimization by metamodel-assisted Nash games, Inria Sophia Antipolis, September 2019, no RR-9290.
https://hal.inria.fr/hal-02285197
[42]
J.-A. Désidéri, R. Duvigneau.
Direct and adaptive approaches to multi-objective optimization, Inria - Sophia Antipolis, September 2019, no RR-9291.
https://hal.inria.fr/hal-02285899

Other Publications

[43]
M. Binois, R. B. Gramacy.
hetGP: Heteroskedastic Gaussian Process Modeling and Sequential Design in R, December 2019, working paper or preprint.
https://hal.inria.fr/hal-02414688
[44]
C. Chalons, S. Kokh, M. Stauffert.
An all-regime and well-balanced Lagrange-projection type scheme for the shallow water equations on unstructured meshes, February 2019, https://arxiv.org/abs/1902.01067 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02004835
[45]
F. A. Chiarello.
An overview of non-local traffic flow models, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02407600
[46]
F. A. Chiarello, J. Friedrich, P. Goatin, S. Göttlich.
Micro-Macro limit of a non-local generalized Aw-Rascle type model, January 2020, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02443123
[47]
R. Duvigneau.
CAD-consistent adaptive refinement using a NURBS-based Discontinuous Galerkin method, November 2019, working paper or preprint.
https://hal.inria.fr/hal-02355979
[48]
N. S. Dymski, P. Goatin, M. D. Rosini.
Modeling moving bottlenecks on road networks, January 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01985837
[49]
M. Garavello, P. Goatin, T. Liard, B. Piccoli.
A controlled multiscale model for traffic regulation via autonomous vehicles, October 2019, https://arxiv.org/abs/1910.04021 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02308788
[50]
N. Laurent-Brouty, G. Costeseque, P. Goatin.
A macroscopic traffic flow model accounting for bounded acceleration, December 2019, working paper or preprint.
https://hal.inria.fr/hal-02155131
[51]
N. Laurent-Brouty, A. Keimer, P. Goatin, A. Bayen.
A macroscopic traffic flow model with finite buffers on networks: Well-posedness by means of Hamilton-Jacobi equations, May 2019, working paper or preprint.
https://hal.inria.fr/hal-02121812
[52]
G. Piacentini, P. Goatin, A. Ferrara.
A macroscopic model for platooning in highway traffic, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02309950
[53]
N. Wycoff, M. Binois, S. M. Wild.
Sequential Learning of Active Subspaces, November 2019, https://arxiv.org/abs/1907.11572 - working paper or preprint.
https://hal.inria.fr/hal-02367750
References in notes
[54]
R. Abgrall, P. M. Congedo.
A semi-intrusive deterministic approach to uncertainty quantification in non-linear fluid flow problems, in: J. Comput. Physics, 2012.
[55]
A. Aggarwal, R. M. Colombo, P. Goatin.
Nonlocal systems of conservation laws in several space dimensions, in: SIAM Journal on Numerical Analysis, 2015, vol. 52, no 2, pp. 963-983.
https://hal.inria.fr/hal-01016784
[56]
G. Alessandrini.
Examples of instability in inverse boundary-value problems, in: Inverse Problems, 1997, vol. 13, no 4, pp. 887–897.
http://dx.doi.org/10.1088/0266-5611/13/4/001
[57]
L. Almeida, P. Bagnerini, A. Habbal.
Modeling actin cable contraction, in: Comput. Math. Appl., 2012, vol. 64, no 3, pp. 310–321.
http://dx.doi.org/10.1016/j.camwa.2012.02.041
[58]
L. Almeida, P. Bagnerini, A. Habbal, S. Noselli, F. Serman.
A Mathematical Model for Dorsal Closure, in: Journal of Theoretical Biology, January 2011, vol. 268, no 1, pp. 105-119. [ DOI : 10.1016/j.jtbi.2010.09.029 ]
http://hal.inria.fr/inria-00544350/en
[59]
D. Amadori, W. Shen.
An integro-differential conservation law arising in a model of granular flow, in: J. Hyperbolic Differ. Equ., 2012, vol. 9, no 1, pp. 105–131.
[60]
P. Amorim.
On a nonlocal hyperbolic conservation law arising from a gradient constraint problem, in: Bull. Braz. Math. Soc. (N.S.), 2012, vol. 43, no 4, pp. 599–614.
[61]
P. Amorim, R. M. Colombo, A. Teixeira.
On the Numerical Integration of Scalar Nonlocal Conservation Laws, in: ESAIM M2AN, 2015, vol. 49, no 1, pp. 19–37.
[62]
M. Annunziato, A. Borzì.
A Fokker-Planck control framework for multidimensional stochastic processes, in: Journal of Computational and Applied Mathematics, 2013, vol. 237, pp. 487-507.
[63]
A. Belme, F. Alauzet, A. Dervieux.
Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows, in: J. Comput. Physics, 2012, vol. 231, no 19, pp. 6323–6348.
[64]
S. Benzoni-Gavage, R. M. Colombo, P. Gwiazda.
Measure valued solutions to conservation laws motivated by traffic modelling, in: Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 2006, vol. 462, no 2070, pp. 1791–1803.
[65]
E. Bertino, R. Duvigneau, P. Goatin.
Uncertainties in traffic flow and model validation on GPS data, 2015.
[66]
F. Betancourt, R. Bürger, K. H. Karlsen, E. M. Tory.
On nonlocal conservation laws modelling sedimentation, in: Nonlinearity, 2011, vol. 24, no 3, pp. 855–885.
[67]
M. Binois, V. Picheny, P. Taillandier, A. Habbal.
The Kalai-Smorodinski solution for many-objective Bayesian optimization, in: BayesOpt workshop at NIPS 2017 - 31st Conference on Neural Information Processing Systems, Long Beach, United States, December 2017, pp. 1-6.
https://hal.inria.fr/hal-01656393
[68]
S. Blandin, P. Goatin.
Well-posedness of a conservation law with non-local flux arising in traffic flow modeling, in: Numer. Math., 2016, vol. 132, no 2, pp. 217–241.
https://doi.org/10.1007/s00211-015-0717-6
[69]
J. Borggaard, J. Burns.
A {PDE} Sensitivity Equation Method for Optimal Aerodynamic Design, in: Journal of Computational Physics, 1997, vol. 136, no 2, pp. 366–384. [ DOI : 10.1006/jcph.1997.5743 ]
http://www.sciencedirect.com/science/article/pii/S0021999197957430
[70]
R. Bourguet, M. Brazza, G. Harran, R. El Akoury.
Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies, in: J. of Fluids and Structures, 2008, vol. 24, no 8, pp. 1240–1251.
[71]
A. Bressan, S. Čanić, M. Garavello, M. Herty, B. Piccoli.
Flows on networks: recent results and perspectives, in: EMS Surv. Math. Sci., 2014, vol. 1, no 1, pp. 47–111.
[72]
M. Burger, M. Di Francesco, P. A. Markowich, M.-T. Wolfram.
Mean field games with nonlinear mobilities in pedestrian dynamics, in: Discrete Contin. Dyn. Syst. Ser. B, 2014, vol. 19, no 5, pp. 1311–1333.
[73]
M. Burger, J. Haskovec, M.-T. Wolfram.
Individual based and mean-field modelling of direct aggregation, in: Physica D, 2013, vol. 260, pp. 145–158.
[74]
A. Cabassi, P. Goatin.
Validation of traffic flow models on processed GPS data, 2013, Research Report RR-8382.
https://hal.inria.fr/hal-00876311
[75]
J. A. Carrillo, S. Martin, M.-T. Wolfram.
A local version of the Hughes model for pedestrian flow, 2015, Preprint.
[76]
K. Chahour, R. Aboulaich, A. Habbal, N. Zemzemi, C. Abdelkhirane.
Virtual FFR quantified with a generalized flow model using Windkessel boundary conditions ; Application to a patient-specific coronary tree, in: Computational and Mathematical Methods in Medicine, 2020.
https://hal.inria.fr/hal-02427411
[77]
C. Chalons, M. L. Delle Monache, P. Goatin.
A conservative scheme for non-classical solutions to a strongly coupled PDE-ODE problem, 2015, Preprint.
[78]
F. A. Chiarello, P. Goatin, L. M. Villada.
High-order Finite Volume WENO schemes for non-local multi-class traffic flow models, in: XVII International Conference on Hyperbolic Problems Theory, Numerics, Applications, University Park, Pennsylvania, United States, June 2018.
https://hal.archives-ouvertes.fr/hal-01979543
[79]
C. Claudel, A. M. Bayen.
Lax-Hopf Based Incorporation of Internal Boundary Conditions Into Hamilton-Jacobi Equation. Part II: Computational Methods, in: Automatic Control, IEEE Transactions on, May 2010, vol. 55, no 5, pp. 1158-1174.
[80]
C. G. Claudel, A. M. Bayen.
Convex formulations of data assimilation problems for a class of Hamilton-Jacobi equations, in: SIAM J. Control Optim., 2011, vol. 49, no 2, pp. 383–402.
[81]
R. M. Colombo, M. Garavello, M. Lécureux-Mercier.
A Class Of Nonloval Models For Pedestrian Traffic, in: Mathematical Models and Methods in Applied Sciences, 2012, vol. 22, no 04, 1150023 p.
[82]
R. M. Colombo, M. Herty, M. Mercier.
Control of the continuity equation with a non local flow, in: ESAIM Control Optim. Calc. Var., 2011, vol. 17, no 2, pp. 353–379.
[83]
R. M. Colombo, M. Lécureux-Mercier.
Nonlocal crowd dynamics models for several populations, in: Acta Math. Sci. Ser. B Engl. Ed., 2012, vol. 32, no 1, pp. 177–196.
[84]
R. M. Colombo, F. Marcellini.
A mixed ODE-PDE model for vehicular traffic, in: Mathematical Methods in the Applied Sciences, 2015, vol. 38, no 7, pp. 1292–1302.
[85]
R. M. Colombo, E. Rossi.
On the micro-macro limit in traffic flow, in: Rend. Semin. Mat. Univ. Padova, 2014, vol. 131, pp. 217–235.
[86]
G. Costeseque, J.-P. Lebacque.
Discussion about traffic junction modelling: conservation laws vs Hamilton-Jacobi equations, in: Discrete Contin. Dyn. Syst. Ser. S, 2014, vol. 7, no 3, pp. 411–433.
[87]
G. Crippa, M. Lécureux-Mercier.
Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow, in: Nonlinear Differential Equations and Applications NoDEA, 2012, pp. 1-15.
[88]
E. Cristiani, B. Piccoli, A. Tosin.
How can macroscopic models reveal self-organization in traffic flow?, in: Decision and Control (CDC), 2012 IEEE 51st Annual Conference on, Dec 2012, pp. 6989-6994.
[89]
E. Cristiani, B. Piccoli, A. Tosin.
Multiscale modeling of pedestrian dynamics, MS&A. Modeling, Simulation and Applications, Springer, Cham, 2014, vol. 12.
[90]
T. Cuisset, J. QuiliCi, G. Cayla..
Qu'est-ce que la FFR? Comment l'utiliser?, in: Réalités Cardiologiques, Janvier/Février 2013.
[91]
C. M. Dafermos.
Solutions in L for a conservation law with memory, in: Analyse mathématique et applications, Montrouge, Gauthier-Villars, 1988, pp. 117–128.
[92]
P. Degond, J.-G. Liu, C. Ringhofer.
Large-scale dynamics of mean-field games driven by local Nash equilibria, in: J. Nonlinear Sci., 2014, vol. 24, no 1, pp. 93–115.
http://dx.doi.org/10.1007/s00332-013-9185-2
[93]
M. L. Delle Monache, P. Goatin.
A front tracking method for a strongly coupled PDE-ODE system with moving density constraints in traffic flow, in: Discrete Contin. Dyn. Syst. Ser. S, 2014, vol. 7, no 3, pp. 435–447.
[94]
M. L. Delle Monache, P. Goatin.
Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result, in: J. Differential Equations, 2014, vol. 257, no 11, pp. 4015–4029.
[95]
B. Després, G. Poëtte, D. Lucor.
Robust uncertainty propagation in systems of conservation laws with the entropy closure method, in: Uncertainty quantification in computational fluid dynamics, Lect. Notes Comput. Sci. Eng., Springer, Heidelberg, 2013, vol. 92, pp. 105–149.
[96]
M. Di Francesco, M. D. Rosini.
Rigorous Derivation of Nonlinear Scalar Conservation Laws from Follow-the-Leader Type Models via Many Particle Limit, in: Archive for Rational Mechanics and Analysis, 2015.
[97]
R. J. DiPerna.
Measure-valued solutions to conservation laws, in: Arch. Rational Mech. Anal., 1985, vol. 88, no 3, pp. 223–270.
[98]
C. Dogbé.
Modeling crowd dynamics by the mean-field limit approach, in: Math. Comput. Modelling, 2010, vol. 52, no 9-10, pp. 1506–1520.
[99]
R. Duvigneau.
A Sensitivity Equation Method for Unsteady Compressible Flows: Implementation and Verification, Inria Research Report No 8739, June 2015.
[100]
R. Duvigneau, D. Pelletier.
A sensitivity equation method for fast evaluation of nearby flows and uncertainty analysis for shape parameters, in: Int. J. of Computational Fluid Dynamics, August 2006, vol. 20, no 7, pp. 497–512.
[101]
J.-A. Désidéri.
Split of Territories in Concurrent Optimization, Inria, October 2007, no 6108, 34 p, https://hal.inria.fr/inria-00127194.
[102]
J.-A. Désidéri.
Multiple-gradient descent algorithm (MGDA) for multiobjective optimization, in: Comptes Rendus de l'Académie des Sciences Paris, 2012, vol. 350, pp. 313-318.
http://dx.doi.org/10.1016/j.crma.2012.03.014
[103]
J.-A. Désidéri.
1, in: Multiple-Gradient Descent Algorithm (MGDA) for Pareto-Front Identification, Modeling, Simulation and Optimization for Science and Technology, Fitzgibbon, W.; Kuznetsov, Y.A.; Neittaanmäki, P.; Pironneau, O. Eds., Springer-Verlag, 2014, vol. 34, J. Périaux and R. Glowinski Jubilees.
[104]
J.-A. Désidéri.
Révision de l'algorithme de descente à gradients multiples (MGDA) par orthogonalisation hiérarchique, Inria, April 2015, no 8710.
[105]
J.-A. Désidéri, R. Duvigneau, A. Habbal.
, Multiobjective Design Optimization using Nash GamesM. Vasile, V. M. Becerra (editors), Progress in Astronautics and Aeronautics, American Institute of Aeronautics and Astronautics (AIAA), Reston, Virginia, 2014, pp. 583–641.
http://dx.doi.org/10.2514/5.9781624102714.0583.0642
[106]
R. Erban, M. B. Flegg, G. A. Papoian.
Multiscale stochastic reaction-diffusion modeling: application to actin dynamics in filopodia, in: Bull. Math. Biol., 2014, vol. 76, no 4, pp. 799–818.
http://dx.doi.org/10.1007/s11538-013-9844-3
[107]
R. Etikyala, S. Göttlich, A. Klar, S. Tiwari.
Particle methods for pedestrian flow models: from microscopic to nonlocal continuum models, in: Math. Models Methods Appl. Sci., 2014, vol. 24, no 12, pp. 2503–2523.
[108]
R. Eymard, T. Gallouët, R. Herbin.
Finite volume methods, in: Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, North-Holland, Amsterdam, 2000, pp. 713–1020.
[109]
R. Farooqui, G. Fenteany.
Multiple rows of cells behind an epithelial wound edge extend cryptic lamellipodia to collectively drive cell-sheet movement, in: Journal of Cell Science, 2005, vol. 118, no Pt 1, pp. 51-63.
[110]
U. Fjordholm, R. Kappeli, S. Mishra, E. Tadmor.
Construction of approximate entropy measure valued solutions for systems of conservation laws, Seminar for Applied Mathematics, ETH Zürich, 2014, no 2014-33.
[111]
M. B. Flegg, S. Hellander, R. Erban.
Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations, in: J. Comput. Phys., 2015, vol. 289, pp. 1–17.
http://dx.doi.org/10.1016/j.jcp.2015.01.030
[112]
F. Fleuret, D. Geman.
Graded learning for object detection, in: Proceedings of the workshop on Statistical and Computational Theories of Vision of the IEEE international conference on Computer Vision and Pattern Recognition (CVPR/SCTV), 1999, vol. 2.
[113]
B. Franz, M. B. Flegg, S. J. Chapman, R. Erban.
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics, in: SIAM J. Appl. Math., 2013, vol. 73, no 3, pp. 1224–1247.
[114]
M. Garavello, B. Piccoli.
Traffic flow on networks, AIMS Series on Applied Mathematics, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2006, vol. 1, Conservation laws models.
[115]
M. Garavello, B. Piccoli.
Coupling of microscopic and phase transition models at boundary, in: Netw. Heterog. Media, 2013, vol. 8, no 3, pp. 649–661.
[116]
P. Goatin, M. Mimault.
A mixed system modeling two-directional pedestrian flows, in: Math. Biosci. Eng., 2015, vol. 12, no 2, pp. 375–392.
[117]
P. Goatin, F. Rossi.
A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit, 2015, Preprint.
http://arxiv.org/abs/1510.04461
[118]
P. Goatin, S. Scialanga.
Well-posedness and finite volume approximations of the LWR traffic flow model with non-local velocity, in: Netw. Heterog. Media, 2016, vol. 11, no 1, pp. 107–121.
[119]
A. Griewank.
Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, in: Optimization Methods and Software, 1992, vol. 1, pp. 35-54.
[120]
M. Gröschel, A. Keimer, G. Leugering, Z. Wang.
Regularity theory and adjoint-based optimality conditions for a nonlinear transport equation with nonlocal velocity, in: SIAM J. Control Optim., 2014, vol. 52, no 4, pp. 2141–2163.
[121]
S. Göttlich, S. Hoher, P. Schindler, V. Schleper, A. Verl.
Modeling, simulation and validation of material flow on conveyor belts, in: Applied Mathematical Modelling, 2014, vol. 38, no 13, pp. 3295–3313.
[122]
A. Habbal, H. Barelli, G. Malandain.
Assessing the ability of the 2D Fisher-KPP equation to model cell-sheet wound closure, in: Math. Biosci., 2014, vol. 252, pp. 45–59.
http://dx.doi.org/10.1016/j.mbs.2014.03.009
[123]
A. Habbal, M. Kallel.
Neumann-Dirichlet Nash strategies for the solution of elliptic Cauchy problems, in: SIAM J. Control Optim., 2013, vol. 51, no 5, pp. 4066–4083.
[124]
X. Han, P. Sagaut, D. Lucor.
On sensitivity of RANS simulations to uncertain turbulent inflow conditions, in: Computers & Fluids, 2012, vol. 61, no 2-5.
[125]
D. Helbing.
Traffic and related self-driven many-particle systems, in: Rev. Mod. Phys., 2001, vol. 73, pp. 1067–1141.
[126]
D. Helbing, P. Molnar, I. J. Farkas, K. Bolay.
Self-organizing pedestrian movement, in: Environment and planning B, 2001, vol. 28, no 3, pp. 361–384.
[127]
J. C. Herrera, D. B. Work, R. Herring, X. J. Ban, Q. Jacobson, A. M. Bayen.
Evaluation of traffic data obtained via GPS-enabled mobile phones: The Mobile Century field experiment, in: Transportation Research Part C: Emerging Technologies, 2010, vol. 18, no 4, pp. 568–583.
[128]
S. P. Hoogendoorn, F. L. van Wageningen-Kessels, W. Daamen, D. C. Duives.
Continuum modelling of pedestrian flows: From microscopic principles to self-organised macroscopic phenomena, in: Physica A: Statistical Mechanics and its Applications, 2014, vol. 416, no 0, pp. 684–694.
[129]
H. Hristova, S. Etienne, D. Pelletier, J. Borggaard.
A continuous sensitivity equation method for time-dependent incompressible laminar flows, in: Int. J. for Numerical Methods in Fluids, 2004, vol. 50, pp. 817-844.
[130]
C. Imbert, R. Monneau.
Flux-limited solutions for quasi-convex Hamilton–Jacobi equations on networks, in: arXiv preprint arXiv:1306.2428, October 2014.
[131]
S. Jeon, H. Choi.
Suboptimal feedback control of flow over a sphere, in: Int. J. of Heat and Fluid Flow, 2010, no 31.
[132]
M. Kallel, R. Aboulaich, A. Habbal, M. Moakher.
A Nash-game approach to joint image restoration and segmentation, in: Appl. Math. Model., 2014, vol. 38, no 11-12, pp. 3038–3053.
http://dx.doi.org/10.1016/j.apm.2013.11.034
[133]
O. Knio, O. Le Maitre.
Uncertainty propagation in CFD using polynomial chaos decomposition, in: Fluid Dynamics Research, September 2006, vol. 38, no 9, pp. 616–640.
[134]
A. Kurganov, A. Polizzi.
Non-Oscillatory Central Schemes for a Traffic Flow Model with Arrehenius Look-Ahead Dynamics, in: Netw. Heterog. Media, 2009, vol. 4, no 3, pp. 431-451.
[135]
A. Lachapelle, M.-T. Wolfram.
On a mean field game approach modeling congestion and aversion in pedestrian crowds, in: Transportation Research Part B: Methodological, 2011, vol. 45, no 10, pp. 1572–1589.
[136]
J.-M. Lasry, P.-L. Lions.
Mean field games, in: Jpn. J. Math., 2007, vol. 2, no 1, pp. 229–260.
[137]
N. Laurent-Brouty, G. Costeseque, P. Goatin.
A coupled PDE-ODE model for bounded acceleration in macroscopic traffic flow models, in: IFAC-PapersOnLine, 2018, vol. 51, no 9, pp. 37–42, 15th IFAC Symposium on Control in Transportation Systems CTS 2018. [ DOI : 10.1016/j.ifacol.2018.07.007 ]
http://www.sciencedirect.com/science/article/pii/S2405896318307237
[138]
M. J. Lighthill, G. B. Whitham.
On kinematic waves. II. A theory of traffic flow on long crowded roads, in: Proc. Roy. Soc. London. Ser. A., 1955, vol. 229, pp. 317–345.
[139]
G. Lin, C.-H. Su, G. Karniadakis.
Predicting shock dynamics in the presence of uncertainties, in: Journal of Computational Physics, 2006, no 217, pp. 260-276.
[140]
M. Martinelli, R. Duvigneau.
On the use of second-order derivative and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics, in: Computers and Fluids, 2010, vol. 37, no 6.
[141]
Q. Mercier, F. Poirion, J. Désidéri.
Non-convex multiobjective optimization under uncertainty: a descent algorithm. Application to sandwich plate design and reliability, in: Engineering Optimization, July 2018, pp. 1-20. [ DOI : 10.1080/0305215X.2018.1486401 ]
https://hal.archives-ouvertes.fr/hal-01870135
[142]
C. Merritt, F. Forsberg, J. Liu, F. Kallel.
In-vivo elastography in animal models: Feasibility studies, (abstract), in: J. Ultrasound Med., 2002, vol. 21, no 98.
[143]
S. Mishra, C. Schwab, J. Sukys.
Multi-level Monte Carlo finite volume methods for uncertainty quantification in nonlinear systems of balance laws, in: Lecture Notes in Computational Science and Engineering, 2013, vol. 92, pp. 225–294.
[144]
P. D. Morris, F. N. van de Vosse, P. V. Lawford, D. R. Hose, J. P. Gunn.
“Virtual”(computed) fractional flow reserve: current challenges and limitations, in: JACC: Cardiovascular Interventions, 2015, vol. 8, no 8, pp. 1009–1017.
[145]
W. Oberkampf, F. Blottner.
Issues in Computational Fluid Dynamics code verification and validation, in: AIAA Journal, 1998, vol. 36, pp. 687–695.
[146]
B. Perthame.
Transport equations in biology, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2007.
[147]
B. Piccoli, F. Rossi.
Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes, in: Acta Appl. Math., 2013, vol. 124, pp. 73–105.
[148]
F. Poirion.
Stochastic Multi Gradient Descent Algorithm, ONERA, July 2014.
[149]
M. Poujade, E. Grasland-Mongrain, A. Hertzog, J. Jouanneau, P. Chavrier, B. Ladoux, A. Buguin, P. Silberzan.
Collective migration of an epithelial monolayer in response to a model wound, in: Proceedings of the National Academy of Sciences, 2007, vol. 104, no 41, pp. 15988-15993.
[150]
F. S. Priuli.
First order mean field games in crowd dynamics, in: ArXiv e-prints, February 2014.
[151]
M. Putko, P. Newman, A. Taylor, L. Green.
Approach for uncertainty propagation and robust design in CFD using sensitivity derivatives, in: 15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, June 2001, AIAA Paper 2001-2528.
[152]
C. Qi, K. Gallivan, P.-A. Absil.
Riemannian BFGS Algorithm with Applications, in: Recent Advances in Optimization and its Applications in Engineering, M. Diehl, F. Glineur, E. Jarlebring, W. Michiels (editors), Springer Berlin Heidelberg, 2010, pp. 183-192.
http://dx.doi.org/10.1007/978-3-642-12598-0_16
[153]
J. Reilly, W. Krichene, M. L. Delle Monache, S. Samaranayake, P. Goatin, A. M. Bayen.
Adjoint-based optimization on a network of discretized scalar conservation law PDEs with applications to coordinated ramp metering, in: J. Optim. Theory Appl., 2015, vol. 167, no 2, pp. 733–760.
[154]
P. I. Richards.
Shock waves on the highway, in: Operations Res., 1956, vol. 4, pp. 42–51.
[155]
P. Sagaut.
Large Eddy Simulation for Incompressible Flows An Introduction, Springer Berlin Heidelberg, 2006.
[156]
J. Schaefer, T. West, S. Hosder, C. Rumsey, J.-R. Carlson, W. Kleb.
Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows, in: 22nd AIAA Computational Fluid Dynamics Conference, 22-26 June 2015, Dallas, USA., 2015.
[157]
V. Schleper.
A hybrid model for traffic flow and crowd dynamics with random individual properties, in: Math. Biosci. Eng., 2015, vol. 12, no 2, pp. 393-413.
[158]
A. Sopasakis, M. A. Katsoulakis.
Stochastic modeling and simulation of traffic flow: asymmetric single exclusion process with Arrhenius look-ahead dynamics, in: SIAM J. Appl. Math., 2006, vol. 66, no 3, pp. 921–944.
[159]
P. R. Spalart.
Detached-Eddy Simulation, in: Annual Review of Fluid Mechanics, 2009, vol. 41, pp. 181-202.
[160]
S. Tokareva, S. Mishra, C. Schwab.
High Order Stochastic Finite Volume Method for the Uncertainty Quantification in Hyperbolic Conservtion Laws with Random Initial Data and Flux Coefficients, in: Proc. ECCOMAS, 2012, Proc. ECCOMAS.
[161]
S. Tu, E. Barbato, Z. Köszegi, J. Yang, Z. Sun, N. Holm, B. Tar, Y. Li, D. Rusinaru, W. Wijns.
Fractional flow reserve calculation from 3-dimensional quantitative coronary angiography and TIMI frame count: a fast computer model to quantify the functional significance of moderately obstructed coronary arteries, in: JACC: Cardiovascular Interventions, 2014, vol. 7, no 7, pp. 768–777.
[162]
É. Turgeon, D. Pelletier, J. Borggaard.
Sensitivity and Uncertainty Analysis for Variable Property Flows, in: 39th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan. 2001, AIAA Paper 2001-0139.
[163]
C. Villani.
Topics in optimal transportation, Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2003, vol. 58.
[164]
C. Villani.
Optimal transport, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin, 2009, vol. 338, Old and new.
[165]
R. Walter, L. Huyse.
Uncertainty analysis for fluid mechanics with applications, ICASE, February 2002, no 2002–1.
[166]
D. Xiu, G. Karniadakis.
Modeling uncertainty in flow simulations via generalized Polynomial Chaos, in: Journal of Computational Physics, 2003, no 187, pp. 137-167.
[167]
D. You, P. Moin.
Active control of flow separation over an airfoil using synthetic jets, in: J. of Fluids and Structures, 2008, vol. 24, pp. 1349-1357.
[168]
A. Zerbinati, A. Minelli, I. Ghazlane, J.-A. Désidéri.
Meta-Model-Assisted MGDA for Multi-Objective Functional Optimization, in: Computers and Fluids, 2014, vol. 102, pp. 116-130, http://www.sciencedirect.com/science/article/pii/S0045793014002576#.
[169]
L. van Nunen, F. Zimmermann, P. Tonino, E. Barbato, A. Baumbach, T. Engstrøm, V. Klauss, P. MacCarthy, G. Manoharan, K. Oldroyd.
Fractional flow reserve versus angiography for guidance of PCI in patients with multivessel coronary artery disease (FAME): 5-year follow-up of a randomised controlled trial, in: The Lancet, 2015, vol. 386, no 10006, pp. 1853–1860.