Bayesian Optimization of Bose-Einstein Condensates.

Area of Science:

• Scientific Computing
• Quantum Many-Body Physics
• Machine Learning

Background:

• Numerical simulations are computationally intensive for modeling complex physical phenomena.
• Data-driven methods offer efficient alternatives for scientific modeling.
• Bose-Einstein Condensates (BECs) require accurate modeling of their quantum states.

Purpose of the Study:

• To investigate the application of Gaussian Processes (GPs) for data-driven modeling of BECs.
• To accurately model the ground state wave function of BECs as a function of scattering parameters.
• To assess the efficiency and versatility of GPs compared to traditional methods.

Main Methods:

• Utilized Gaussian Processes (GPs) for data-driven modeling.
• Trained GPs on data from coarse-grained simulations of BECs.
• Investigated GPs for scalar and vectorial BECs under various potentials (harmonic, double well, optical lattice).

Main Results:

• GPs accurately reproduced BEC ground state wave functions with limited simulation data.
• The method demonstrated consistent performance across diverse BEC configurations and potentials.
• Achieved comparable accuracy to existing models using significantly less data ([Formula: see text]th).
• The GP model provides uncertainty quantification for the predictions.

Conclusions:

• Gaussian Processes provide a versatile and efficient data-driven approach for modeling BECs.
• This method significantly reduces data requirements and computational time compared to traditional simulations.
• The approach is generalizable to other quantum many-body problems.