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In this paper, we study simultaneous wireless information and power transfer (SWIPT) systems employing practical non-linear energy harvester (EH) circuits. Since the voltage across the reactive elements of realistic EH circuits cannot drop or rise instantaneously, EHs have memory which we model with a Markov decision process (MDP). Moreover, since an analytical model that accurately models all non-linear effects and the unavoidable impedance mismatch of EHs is not tractable, we propose a learning based model for the EH circuit. We optimize the input signal distribution for maximization of the harvested power under a constraint on the minimum mutual information between transmitter (TX) and information receiver (IR). We distinguish the cases where the MDP state is known and not known at TX and IR. When the MDP state is known, the formulated optimization problem for the harvested power is convex. In …