Bakthavatchalam Tamil Arasan, Ramamoorthy Suriyadeepan, Sankarasubbu Malaikannan, Ramaswamy Radha, Sethuraman Vijayalakshmi
Department of Physics, Presidency College (Autonomous), University of Madras, Chennai, 600005, India.
Saama AI Research Lab, Chennai, 600032, India.
Sci Rep. 2021 Mar 3;11(1):5054. doi: 10.1038/s41598-021-84336-0.
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 ([Formula: see text]th) 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 [Formula: see text] 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.
机器学习方法正作为数值模拟技术的更快且高效的替代方法而兴起。科学计算领域已开始采用这些数据驱动的方法，利用基于粗粒度网格模拟的零散、有噪声的观测数据来忠实地模拟物理现象。在本文中，我们研究玻色 - 爱因斯坦凝聚体（BECs）的数据驱动建模。具体而言，我们使用高斯过程（GPs）将BECs的基态波函数建模为无量纲格罗斯 - 皮塔耶夫斯基方程（GPE）中散射参数的函数。实验结果表明，GPs能够使用来自模拟的有限数量的数据点准确地重现基态波函数。在不同配置的BECs（即在不同势场下产生的标量和矢量BECs，包括谐波、双阱和光学晶格势场）中一致的性能表明了我们方法的通用性。与现有数据驱动模型的比较表明，我们的模型仅使用现有方法所用数据点的一小部分（[公式：见正文]）就能达到相似的精度，此外还能对数据中的不确定性进行建模。当用作训练后的模拟器时，我们的模型生成基态波函数[公式：见正文]的速度比使用虚时演化的数值近似技术特罗特 - 铃木方法更快。我们的方法非常通用；只需稍作修改，就可应用于类似的量子多体问题。
