  Machine Learning methods are emerging as faster and efficient alternatives to
numerical simulation techniques. The field of Scientific Computing has started
adopting these data-driven approaches to faithfully model physical phenomena
using scattered, noisy observations from coarse-grained grid-based simulations.
In this paper, we investigate data-driven modelling of Bose-Einstein
Condensates (BECs). In particular, we use Gaussian Processes (GPs) to model the
ground state wave function of BECs as a function of scattering parameters from
the dimensionless Gross Pitaveskii Equation (GPE). Experimental results
illustrate the ability of GPs to accurately reproduce ground state wave
functions using a limited number of data points from simulations. Consistent
performance across different configurations of BECs, namely Scalar and
Vectorial BECs generated under different potentials, including harmonic, double
well and optical lattice potentials pronounces the versatility of our method.
Comparison with existing data-driven models indicates that our model achieves
similar accuracy with only a small fraction 1/50th of data points used by
existing methods, in addition to modelling uncertainty from data. When used as
a simulator post-training, our model generates ground state wave functions $36
\times $ faster than Trotter Suzuki, a numerical approximation technique that
uses Imaginary time evolution. Our method is quite general; with minor changes
it can be applied to similar quantum many-body problems.

Quantum Gases