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

TL;DR

This paper introduces an ANN-based method to efficiently solve the inverse problem of the 1D Gross-Pitaevskii equation, predicting potential and interaction parameters from density data.

Contribution

The paper presents a novel neural network approach that accurately and quickly infers physical parameters of a Bose-Einstein Condensate from its density distribution.

Findings

ANN accurately predicts potential and interaction parameters

Method is fast compared to traditional numerical solutions

Validated on over 30,000 GPE parameter sets

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 (BEC) 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.