G. Wang, F. Wang, G. Magai, Y. Lei, A. Huang et al., Performance comparison of 1200v 100a sic mosfet and 1200v 100a silicon igbt, Energy Conversion Congress and Exposition (ECCE), pp.3230-3234, 2013.

D. Ljubisa, K. S. Stevanovic, . Matocha, A. Peter, J. S. Losee et al., Recent advances in silicon carbide mosfet power devices, Applied Power Electronics Conference and Exposition (APEC), 2010 Twenty-Fifth Annual IEEE, pp.401-407, 2010.

R. Allen and . Hefner, A dynamic electro-thermal model for the igbt, Industry Applications Society Annual Meeting, 1992., Conference Record of the 1992 IEEE, pp.1094-1104, 1992.

J. Ye, K. Yang, H. Ye, and A. Emadi, A fast electro-thermal model of traction inverters for electrified vehicles, IEEE Transactions on Power Electronics, vol.32, issue.5, pp.3920-3934, 2017.

W. Huanhuan, Dynamic Electro-Thermal Model of Power Electronic Building Block in Micro Grid: Modeling, Analysis and Simulation, 2012.

D. Graovac, M. Purschel, and A. Kiep, Mosfet power losses calculation using the data-sheet parameters, 2006.

A. Dustin, J. Murdock, J. J. Torres, R. Connors, and . Lorenz, Active thermal control of power electronic modules, IEEE Transactions on Industry Applications, vol.42, issue.2, pp.552-558, 2006.

M. Pecht, Handbook of electronic package design, vol.76, 1991.

J. Arwidson, Thermal Fatigue Life Prediction of Solder Joints in Avionics by Surrogate Modeling: A Contribution to Physics of Failure in Reliability Prediction, 2013.

M. Handbook, Electronic reliability design handbook, 1988.

P. Lall, M. Pecht, and E. Hakim, Influence of temperature on microelectronics and system reliability: A physics of failure approach, 1997.

M. Douglas-a-pietila, K. Rassaian, and . Brice-heames, Design characterization of microwave antenna bga interconnect structure using test-validated physics-of-failure methods, Reliability Physics Symposium Proceedings, 1999. 37th Annual. 1999 IEEE International, pp.347-355, 1999.

L. Theodore, . Bergman, P. Frank, . Incropera, P. David et al., Fundamentals of heat and mass transfer, 2011.

V. Buljak, Inverse analyses with model reduction: proper orthogonal decomposition in structural mechanics, 2011.

V. Buljak and G. Maier, Proper orthogonal decomposition and radial basis functions in material characterization based on instrumented indentation. Engineering Structures, vol.33, pp.492-501, 2011.

V. Buljak, Proper orthogonal decomposition and radial basis functions algorithm for diagnostic procedure based on inverse analysis, FME Transactions, vol.38, issue.3, pp.129-136, 2010.

G. Bolzon and V. Buljak, An effective computational tool for parametric studies and identification problems in materials mechanics, Computational mechanics, vol.48, issue.6, pp.675-687, 2011.

D. Xiao, . Fang, G. Pain, and . Hu, Non-intrusive reduced-order modelling of the navierstokes equations based on rbf interpolation, International Journal for Numerical Methods in Fluids, vol.79, issue.11, pp.580-595, 2015.

Z. Lin, . Xiao, and . Fang, Non-intrusive reduced order modelling with least squares fitting on a sparse grid, CC Pain, and Ionel M Navon, vol.83, pp.291-306, 2017.

K. Pearson and . Liii, on lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine, Journal of Science, vol.2, issue.11, pp.559-572, 1901.

H. Gene, C. Golub, and . Loan, Matrix computations, vol.3, 2012.

. Gml-gladwell, Branch mode analysis of vibrating systems, Journal of sound and vibration, vol.1, issue.1, pp.41-59, 1964.

A. Neveu, K. El-khoury, and B. Flament, Simulation de la conduction non linéaire en régime variable: décomposition sur les modes de branche, International journal of thermal sciences, vol.38, issue.4, pp.289-304, 1999.

O. Quéméner, F. Joly, and A. Neveu, The generalized amalgam method for modal reduction, International Journal of Heat and Mass Transfer, vol.55, issue.4, pp.1197-1207, 2012.

O. Quemener, A. Neveu, and E. Videcoq, A specific reduction method for the branch modal formulation: Application to a highly non-linear configuration, International journal of thermal sciences, vol.46, issue.9, pp.890-907, 2007.

Y. Yang and W. Chen, A nonlinear inverse problem in estimating the heat flux of the disc in a disc brake system, Applied Thermal Engineering, pp.2439-2448, 2011.

. Sr-carvalho, . Lima-e-silva, G. Machado, and . Guimaraes, Temperature determination at the chip-tool interface using an inverse thermal model considering the tool and tool holder, Journal of Materials Processing Technology, vol.179, issue.1-3, pp.97-104, 2006.

P. Dimitri and . Bertsekas, Constrained optimization and Lagrange multiplier methods, 2014.

H. Everett and I. , Generalized lagrange multiplier method for solving problems of optimum allocation of resources, Operations research, vol.11, issue.3, pp.399-417, 1963.

Y. Evtushenko, Generalized lagrange multiplier technique for nonlinear programming, Journal of Optimization Theory and Applications, vol.21, issue.2, pp.121-135, 1977.

C. Homescu, R. Linda, R. Petzold, and . Serban, Error estimation for reduced-order models of dynamical systems, SIAM Journal on Numerical Analysis, vol.43, issue.4, pp.1693-1714, 2005.

M. Müller, On the POD method: an abstract investigation with applications to reduced-order modeling and suboptimal control, 2008.

D. Amsallem, J. Cortial, K. Carlberg, and C. Farhat, A method for interpolating on manifolds structural dynamics reduced-order models, International journal for numerical methods in engineering, vol.80, issue.9, pp.1241-1258, 2009.

D. Amsallem and C. Farhat, Interpolation method for adapting reduced-order models and application to aeroelasticity, AIAA journal, vol.46, issue.7, pp.1803-1813, 2008.

T. Lieu and M. Lesoinne, Parameter adaptation of reduced order models for threedimensional flutter analysis, 42nd AIAA Aerospace Sciences Meeting and Exhibit, p.888, 2004.

K. Carlberg, C. Bou-mosleh, and C. Farhat, Efficient non-linear model reduction via a least-squares petrov-galerkin projection and compressive tensor approximations, International Journal for Numerical Methods in Engineering, vol.86, issue.2, pp.155-181, 2011.

K. Willcox, Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Computers & fluids, vol.35, issue.2, pp.208-226, 2006.

R. Everson and L. Sirovich, Karhunen-loeve procedure for gappy data, JOSA A, vol.12, issue.8, pp.1657-1664, 1995.

T. Bui-thanh, M. Damodaran, and K. E. Willcox, Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition, AIAA journal, vol.42, issue.8, pp.1505-1516, 2004.

T. Bui-thanh, M. Damodaran, and K. Willcox, Proper orthogonal decomposition extensions for parametric applications in compressible aerodynamics, 21st AIAA Applied Aerodynamics Conference, p.4213, 2003.

E. Nathan, L. S. Murray, and . Ukeiley, An application of gappy pod, Experiments in Fluids, vol.42, issue.1, pp.79-91, 2007.

M. Ho, Y. Tong, C. P. Lai, and . Wong, Advanced flip chip packaging, 2013.

D. Cheikh-tidiane, Génération de modeles compacts thermiques dynamiques de composants electroniques via les algorithmes genetiques, vol.10, 2015.

. Ph-mellor, . Roberts, and . Turner, Lumped parameter thermal model for electrical machines of tefc design, IEE Proceedings B (Electric Power Applications), vol.138, pp.205-218, 1991.

M. Ayman, . El-refaie, C. Nathan, . Harris, M. Thomas et al., Thermal analysis of multibarrier interior pm synchronous machine using lumped parameter model, IEEE Transactions on Energy Conversion, vol.19, issue.2, pp.303-309, 2004.

X. Lin, H. E. Perez, S. Mohan, J. B. Siegel, A. G. Stefanopoulou et al., A lumped-parameter electro-thermal model for cylindrical batteries, Journal of Power Sources, vol.257, pp.1-11, 2014.

S. Nategh, O. Wallmark, M. Leksell, and S. Zhao, Thermal analysis of a pmasrm using partial fea and lumped parameter modeling, IEEE Transactions on Energy Conversion, vol.27, issue.2, pp.477-488, 2012.

C. Forgez, D. Vinh-do, and G. Friedrich, Mathieu Morcrette, and Charles Delacourt. Thermal modeling of a cylindrical lifepo4/graphite lithium-ion battery, Journal of Power Sources, vol.195, issue.9, pp.2961-2968, 2010.

M. Ishizuka, T. Hatakeyama, and Y. Funawatashi, Application of thermal network model to transient thermal analysis of power electronic package substrate. Active and Passive Electronic Components, 2011.

N. Francesc and . Masana, A closed form solution of junction to substrate thermal resistance in semiconductor chips, IEEE Transactions on Components, Packaging, and Manufacturing Technology: Part A, vol.19, issue.4, pp.539-545, 1996.

. Sm-thompson and . Ma, Thermal spreading analysis of rectangular heat spreader, Journal of Heat Transfer, vol.136, issue.6, p.64503, 2014.

. Fn-masana, A straightforward analytical method for extraction of semiconductor device transient thermal parameters. Microelectronics Reliability, vol.47, pp.2122-2128, 2007.

A. Raciti, D. Cristaldi, G. Greco, G. Vinci, and G. Bazzano, Electrothermal pspice modeling and simulation of power modules, IEEE Transactions on Industrial Electronics, vol.62, issue.10, pp.6260-6271, 2015.

Y. Michael, Four decades of research on thermal contact, gap, and joint resistance in microelectronics, IEEE transactions on components and packaging technologies, vol.28, pp.182-206, 2005.

M. Ho, Y. Tong, C. P. Lai, and . Wong, Advanced flip chip packaging, 2013.

. Fn-masana, A new approach to the dynamic thermal modelling of semiconductor packages, Microelectronics Reliability, vol.41, pp.901-912, 2001.

V. Székely and T. Van-bien, Fine structure of heat flow path in semiconductor devices: a measurement and identification method, Solid-State Electronics, vol.31, issue.9, pp.1363-1368, 1988.

M. Ciappa, W. Fichtner, Y. Kojima, Y. Yamada, and . Nishibe, Extraction of accurate thermal compact models for fast electro-thermal simulation of igbt modules in hybrid electric vehicles, Microelectronics Reliability, vol.45, pp.1694-1699, 2005.

G. Yu, B. Yu, D. Han, and L. Wang, Unsteady-state thermal calculation of buried oil pipeline using a proper orthogonal decomposition reduced-order model, Applied Thermal Engineering, vol.51, issue.1-2, pp.177-189, 2013.

A. Fic, A. Ryszard, A. J. Bia?ecki, and . Kassab, Solving transient nonlinear heat conduction problems by proper orthogonal decomposition and the finite-element method. Numerical Heat Transfer, Part B: Fundamentals, vol.48, issue.2, pp.103-124, 2005.

J. Hazem-ben-aissia, R. Jay, S. Knikker, and . Xin, Modèle thermique réduit appliqué à une carte électronique de puissance, Société Française de Thermique, 2017.

. Sr-carvalho, . Lima-e-silva, G. Machado, and . Guimaraes, Temperature determination at the chip-tool interface using an inverse thermal model considering the tool and tool holder, Journal of Materials Processing Technology, vol.179, issue.1-3, pp.97-104, 2006.

M. Girault and D. Petit, Identification methods in nonlinear heat conduction. part i: Model reduction, International Journal of Heat and Mass Transfer, vol.48, issue.1, pp.105-118, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017512

M. Girault and D. Petit, Identification methods in nonlinear heat conduction. part ii: inverse problem using a reduced model, International Journal of Heat and Mass Transfer, vol.48, issue.1, pp.119-133, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00017512

E. Videcoq, M. Lazard, O. Quemener, and A. Neveu, Online temperature prediction using a branch eigenmode reduced model applied to cutting process, Numerical Heat Transfer, Part A: Applications, vol.55, issue.7, pp.683-705, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01180010

H. Gene, C. Golub, and . Loan, Matrix computations, vol.3, 2012.