Phenomenological model of superconducting optoelectronic loop neurons

Superconducting optoelectronic loop neurons are a class of circuits potentially conducive to networks for large-scale artificial cognition. These employ superconducting components including single-photon detectors, Josephson junctions, and transformers achieve neuromorphic functions. To date, all simulations have used first-principles circuit analysis model the behavior synapses, dendrites, neurons. models computationally inefficient leave opaque relationship between other complex systems. Here we introduce modeling framework that captures relevant synaptic, dendritic, neuronal at phenomenological level without resorting full equations. Within this compact model, each dendrite is discovered obey single nonlinear leaky-integrator ordinary differential equation, while neuron modeled as with thresholding element an additional feedback mechanism establishing refractory period. A synapse detector coupled dendrite, where response follows closed-form expression. We quantify accuracy relative find approach reduces computational time by factor ten thousand maintaining one part in thousand. demonstrate use several basic examples. The net increase efficiency enables future simulation large networks, formulation provides connection body work applied mathematics, neuroscience, physical systems such spin glasses.