Nonlinear memristor model with exact solution allows for <i>ex situ</i> reservoir computing training and <i>in situ</i> inference

Memristive physical reservoir computing is a promising approach for solving data classification and temporal processing tasks. This method exploits the nonlinear dynamics of physical, low-power devices to achieve high-dimensional mapping of input signals. Ion-channel-based memristors, which operate with similar voltages, currents, and timescales as biological synapses, are promising due to their rich dynamics, especially for use in biological edge settings. Accurate modeling of their dynamics is essential for optimizing network hyperparameters <i>ex situ</i> to save time and energy. Here, a generalized sigmoidal growth model of ion-channel memristor conductance is presented and shown to be more accurate in predicting dynamics than linear or logistic models. Using the exact solution of the proposed sigmoidal model, the MNIST handwritten digit classification task is optimized and trained <i>ex situ</i>, then tested <i>in situ</i> with the same trained weights. This approach achieved an experimental testing accuracy of 90.6%.