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Compute intensive kernels make up the majority of execution time in HPC applications. Therefore, many of the power draw and energy consumption traits of HPC applications can be characterized in terms of the power draw and energy consumption of these constituent kernels. Given that power and energy-related constraints have emerged as major design impediments for exascale systems, it is crucial to develop a greater understanding of how kernels behave in terms of power/energy when subjected to different compiler-based optimizations and different hardware settings. In this work, we develop CPU and DIMM power and energy models for three extensively utilized HPC kernels by training artificial neural networks. These networks are trained using empirical data gathered on the target architecture. The models utilize kernel-specific compiler-based optimization parameters and hard-ware tunables as inputs and make predictions for the power draw rate and energy consumption of system components. The resulting power draw and energy usage predictions have an absolute error rate that averages less than 5.5% for three important kernels - matrix multiplication (MM), stencil computation and LU factorization.