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Superconducting optoelectronic loop neurons are a class of circuitspotentially conducive to networks for large-scale artificial cognition. Thesecircuits employ superconducting components including single-photon detectors,Josephson junctions, and transformers to achieve neuromorphic functions. Todate, all simulations of loop neurons have used first-principles circuitanalysis to model the behavior of synapses, dendrites, and neurons. Thesecircuit models are computationally inefficient and leave opaque therelationship between loop neurons and other complex systems. Here we introducea modeling framework that captures the behavior of the relevant synaptic,dendritic, and neuronal circuits at a phenomenological level without resortingto full circuit equations. Within this compact model, each dendrite isdiscovered to obey a single nonlinear leaky-integrator ordinary differentialequation, while a neuron is modeled as a dendrite with a thresholding elementand an additional feedback mechanism for establishing a refractory period. Asynapse is modeled as a single-photon detector coupled to a dendrite, where theresponse of the single-photon detector follows a closed-form expression. Wequantify the accuracy of the phenomenological model relative to circuitsimulations and find that the approach reduces computational time by a factorof ten thousand while maintaining accuracy of one part in ten thousand. Wedemonstrate the use of the model with several basic examples. The net increasein computational efficiency enables future simulation of large networks, whilethe formulation provides a connection to a large body of work in appliedmathematics, computational neuroscience, and physical systems such as spinglasses.

Phenomenological Model of Superconducting Optoelectronic Loop Neurons