Large scale scientific applications in general and especially cardiac simulations experience different execution phases at runtime and each phase has different computational and communication requirements. An optimal solution or numerical scheme for one execution phase might not be appropriate for the next phase of the application execution. We propose an autonomic management framework, which is built on the physics aware programming (PAP) paradigm for accelerating the cardiac simulations further beyond what can be achieved through traditional parallelization efforts. This approach effectively exploits the physical properties of the cardiac simulation by being smart in the development of simulation algorithms. The cardiac simulation phase is periodically monitored and analyzed to identify its current execution phase. We apply machine learning techniques to detect the phase of the simulation during each time step of the 3D model of a human ventricular epicardial myocyte simulation. For each change in the simulation phase, we exploit the spatial and temporal attributes, dynamically change the resolution of the simulation, and select the numerical algorithms/solvers that optimize its performance without sacrificing the accuracy of the simulation. We compare the performance of the PAP-based algorithm in terms of simulation accuracy and execution time with respect to the reference simulation, which is considered the high-precision implementation. We achieve an overall speedup of 28.4× with a simulation accuracy of 99.9% with the PAP-based cardiac simulations. We also couple the PAP with a multi-graphics processing units (GPU) implementation, and show up to 191× speedup on a 16-GPU system.