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We propose a new physical basis for energy efficient implementation of artificial neural network (ANN) algorithms. These are two neuron cells: Sigma-cell and Gauss-cell with sigmoid- and Gaussian-like activation functions respectively. We optimize their parameters for application in three-layer perceptron and radial basis functions networks. Design of these cells is inspired by adiabatic quantum flux parametron (AQFP); the both have simple topology and low energy consumption, working in superconducting regime. Maintained similarity of designs allows the using of well-developed adiabatic superconductor logic cells in interface circuits. Their performance was further optimized by introduction of Josephson heterostructures with weak links composed of superconductor, isolator and ferromagnetic metal.