An application of neurohydrodynamics to a Hopfield neural network

In this paper, we apply our approach of Neurohydrodynamics (NHD) to a Hopfield neural network by introducing a one-dimensional spacial diffusion term. This reaction-diffusion equation includes an auxiliary equation that “guides” the weights of the network using the divergence of neuron´s activation amplitude, which we call the neuropotential. This guiding principle is similar to de Broglie´s “pilot wave” interpretation for Quantum Mechanics or Turing´s oracle for “human intuition” of a Turing machine. Finally, using a numerical derivation of the dynamical equations of one-dimensional Hopfield neural network, we include a simulation of the network so that we can discuss its behavior and future directions of NHD.