  Mathematical models of the human heart are increasingly playing a vital role
in understanding the working mechanisms of the heart, both under healthy
functioning and during disease. The aim is to aid medical practitioners
diagnose and treat the many ailments affecting the heart. Towards this,
modelling cardiac electrophysiology is crucial as the heart's electrical
activity underlies the contraction mechanism and the resulting pumping action.
The governing equations and the constitutive laws describing the electrical
activity in the heart are coupled, nonlinear, and involve a fast moving wave
front, which is generally solved by the finite element method. The simulation
of this complex system as part of a virtual heart model is challenging due to
the necessity of fine spatial and temporal resolution of the domain. Therefore,
efficient surrogate models are needed to predict the dynamics under varying
parameters and inputs. In this work, we develop an adaptive, projection-based
surrogate model for cardiac electrophysiology. We introduce an a posteriori
error estimator that can accurately and efficiently quantify the accuracy of
the surrogate model. Using the error estimator, we systematically update our
surrogate model through a greedy search of the parameter space. Furthermore,
using the error estimator, the parameter search space is dynamically updated
such that the most relevant samples get chosen at every iteration. The proposed
adaptive surrogate modelling technique is tested on three benchmark models to
illustrate its efficiency, accuracy, and ability of generalization.
