D. Amsallem and C. Farhat, An Online Method for Interpolating Linear Parametric Reduced-Order Models, SIAM Journal on Scientific Computing, vol.33, issue.5, p.2169, 2011.
DOI : 10.1137/100813051
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.664.9881

H. T. Banks, M. L. Joyner, B. Winchesky, and W. P. Winfree, Nondestructive evaluation using a reduced-order computational methodology, Inverse Problems, vol.16, issue.4, pp.1-17, 2000.
DOI : 10.1088/0266-5611/16/4/304

G. Berkooz, P. Holmes, and J. L. Lumley, The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows, Annual Review of Fluid Mechanics, vol.25, issue.1, pp.539-575, 1993.
DOI : 10.1146/annurev.fl.25.010193.002543

A. Buffa, Y. Maday, A. T. Patera, C. Prud-'homme, and G. Turinici, A priori convergence of the greedy algorithm for the parametrized reduced basis method. ESAIM: M2AN, pp.595-603, 2011056.
URL : https://hal.archives-ouvertes.fr/hal-00659314

R. Chabiniok, P. Moireau, P. Lesault, A. Rahmouni, J. Deux et al., Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model, Biomechanics and Modeling in Mechanobiology, vol.3, issue.4, pp.609-630, 2012.
DOI : 10.1007/s10237-011-0337-8
URL : https://hal.archives-ouvertes.fr/hal-00654541

D. Chapelle and K. J. Bathe, The inf-sup test, Computers & Structures, vol.47, issue.4-5, pp.537-545, 1993.
DOI : 10.1016/0045-7949(93)90340-J
URL : https://hal.archives-ouvertes.fr/hal-00839728

D. Chapelle, A. Gariah, and J. Sainte-marie, Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples, ESAIM: M2AN, pp.731-757, 2012.
DOI : 10.1051/m2an/2011053
URL : https://hal.archives-ouvertes.fr/hal-00654539

D. Chapelle, P. Le-tallec, P. Moireau, and M. Sorine, ENERGY-PRESERVING MUSCLE TISSUE MODEL: FORMULATION AND COMPATIBLE DISCRETIZATIONS, International Journal for Multiscale Computational Engineering, vol.10, issue.2, pp.189-211, 2012.
DOI : 10.1615/IntJMultCompEng.2011002360
URL : https://hal.archives-ouvertes.fr/hal-00678772

G. Chavent, Nonlinear Least Squares for Inverse Problems. Scientific Computation Theoretical foundations and step-by-step guide for applications, 2009.

P. G. Ciarlet and P. A. Raviart, General lagrange and hermite interpolation in Rn with applications to finite element methods, Archive for Rational Mechanics and Analysis, vol.46, issue.3, pp.177-199, 1972.
DOI : 10.1007/BF00252458

R. Fitzhugh, Impulses and Physiological States in Theoretical Models of Nerve Membrane, Biophysical Journal, vol.1, issue.6, pp.445-466, 1961.
DOI : 10.1016/S0006-3495(61)86902-6

D. Galbally, K. Fidkowski, K. Willcox, and O. Ghattas, Non-linear model reduction for uncertainty quantification in large-scale inverse problems, International Journal for Numerical Methods in Engineering, vol.41, issue.2, pp.811581-1608, 2010.
DOI : 10.1002/nme.2086

B. Haasdonk, Convergence Rates of the POD???Greedy Method, ESAIM: Mathematical Modelling and Numerical Analysis, vol.47, issue.3, 2012045.
DOI : 10.1051/m2an/2012045

S. Julier, J. Uhlmann, and H. Durrant-whyte, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Transactions on Automatic Control, vol.45, issue.3, pp.447-482, 2000.
DOI : 10.1109/9.847726

K. Kunisch and S. Volkwein, Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics, SIAM Journal on Numerical Analysis, vol.40, issue.2, pp.492-515, 2002.
DOI : 10.1137/S0036142900382612

A. Manzoni, A. Quarteroni, and G. Rozza, Shape optimization for viscous flows by reduced basis methods and free-form deformation, International Journal for Numerical Methods in Fluids, vol.25, issue.2, 2012.
DOI : 10.1002/fld.2712

P. Moireau and D. Chapelle, Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems, ESAIM: Control, Optimisation and Calculus of Variations, vol.17, issue.2, pp.380-405, 2011.
DOI : 10.1051/cocv/2010006
URL : https://hal.archives-ouvertes.fr/inria-00550104

P. Moireau, D. Chapelle, and P. L. Tallec, Joint state and parameter estimation for distributed mechanical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.659-677, 2008.
DOI : 10.1016/j.cma.2007.08.021
URL : https://hal.archives-ouvertes.fr/hal-00175623

P. Moireau, D. Chapelle, and P. L. Tallec, Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging, Inverse Problems, vol.25, issue.3, p.35010, 2009.
DOI : 10.1088/0266-5611/25/3/035010
URL : https://hal.archives-ouvertes.fr/hal-00358914

J. Nagumo, S. Arimoto, and S. Yoshizawa, An Active Pulse Transmission Line Simulating Nerve Axon, Proceedings of the IRE, pp.2061-2070, 1962.
DOI : 10.1109/JRPROC.1962.288235

D. Pham, J. Verron, and L. Gourdeau, Filtres de Kalman singuliers évolutifs pour l'assimilation de données en océanographie, Comptes Rendus de l'Académie des Sciences - Series IIA, pp.255-260, 1998.
DOI : 10.1016/s1251-8050(97)86815-2

C. Prud-'homme, D. V. Rovas, K. Veroy, L. Machiels, Y. Maday et al., Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, Journal of Fluids Engineering, vol.124, issue.1, pp.70-80, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00798326

J. Sainte-marie, D. Chapelle, R. Cimrman, and M. Sorine, Modeling and estimation of the cardiac electromechanical activity, Computers & Structures, vol.84, issue.28, pp.1743-1759, 2006.
DOI : 10.1016/j.compstruc.2006.05.003
URL : https://hal.archives-ouvertes.fr/hal-00839206

D. Simon, Optimal State Estimation: Kalman, H ? , and Nonlinear Approaches, 2006.
DOI : 10.1002/0470045345

S. A. Smolyak, Quadrature and interpolation formulas for tensor products of certain classes of functions, Dokl. Akad. Nauk SSSR, vol.4, pp.240-243, 1963.

K. Veroy and A. T. Patera, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basisa posteriori error bounds, International Journal for Numerical Methods in Fluids, vol.42, issue.8-9, pp.773-788, 2004.
DOI : 10.1002/fld.867