Solution of inverse problem for Gross-Pitaevskii equation with artificial neural networks

Abstract We propose an artificial neural network (ANN) design to solve the inverse problem for a 1D Gross–Pitaevskii equation (GPE). More precise, the ANN takes the squared modulus of the stationary GPE solution as an input and returns the parameters of the potential function and the factor in front of the GPE non-linear term. From the physical point of view the ANN predicts the parameters of a trap potential and the interaction constant of 1D Bose–Einstein condensate by its density distribution. Using the results of numerical solution of GPE for more than 30 000 sets of GPE parameters as train and validation datasets we build the ANN as a fast and accurate inverse GPE solver.