In this paper, we study the rate-power region of a simultaneous wireless information and power transfer (SWIPT) system where a transmitter (TX) broadcasts a common signal to an information receiver (IR) and an energy harvester (EH). Since practical EH circuits include a reactive element as part of their signal rectifier and the voltage on this element cannot drop or rise instantaneously, the EH circuit has memory. We model the memory effect of the EH by a Markov reward chain. Furthermore, since an analytical model that includes all non-linear and memory effects of the EH circuit is not available, we employ a deep neural network (DNN) to model the Markov chain evolution. We formulate an optimization problem to determine the rate-power region of the considered SWIPT system and propose an iterative algorithm based on sequential quadratic programming (SQP) to solve it. Our numerical results show that the optimal input distribution and the rate-power region depend on both the input power level at the EH and the symbol duration.