Using Artificial Neural Networks to Solve the Gross–Pitaevskii Equation

Abstract

The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials. With the assistance of neural networks, a model is formed that is capable of solving this equation. The adaptation of the parameters for the constructed model is performed using some evolutionary techniques, such as genetic algorithms and particle swarm optimization. The proposed model is used to solve the GPE for the linear case (γ=0) and the nonlinear case (γ≠0), where γ is the nonlinearity parameter in GPE. The results are close to the reported results regarding the behavior and the amplitudes of the wavefunctions.

Keywords

• Gross–Pitaevskii equation
• simulations
• machine learning
• neural