  Clinical oriented applications of computational electrocardiology require
efficient and reliable identification of patient-specific parameters of
mathematical models based on available measures. In particular, the estimation
of cardiac conductivities in models of potential propagation is crucial, since
they have major quantitative impact on the solution. Available estimates of
cardiac conductivities are significantly diverse in the literature and the
definition of experimental/mathematical estimation techniques is an open
problem with important practical implications in clinics. We have recently
proposed a methodology based on a variational procedure, where the reliability
is confirmed by numerical experiments. In this paper we explore
model-order-reduction techniques to fit the estimation procedure into timelines
of clinical interest. Specifically we consider the Monodomain model and resort
to Proper Orthogonal Decomposition (POD) techniques to take advantage of an
off-line step when solving iteratively the electrocardiological forward model
online. In addition, we perform the Discrete Empirical Interpolation Method
(DEIM) to tackle the nonlinearity of the model. While standard POD techniques
usually fail in this kind of problems, due to the wave-front propagation
dynamics, an educated novel sampling of the parameter space based on the
concept of Domain of Effectiveness introduced here dramatically reduces the
computational cost of the inverse solver by at least 95%.
