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.