Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a Green's function or time dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic model decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.
翻译:在本文中,我们讨论了使用动态模型分解(DMD)的可能性,这是一种数据驱动的减少命令模型技术,以利用在小窗口内绘制的短片来描述与无平衡动态有关的一次性可观测数据。DMD方法使我们能够从有限的轨迹样本中有效地预测长期动态。我们展示了DMD在模式二波段系统中的有效性。我们显示,在平衡限度内,DMD分析得出的结果与线性反应分析得出的结果一致。在无平衡性案例中,DMD产生的外推式动态比本文提出的一个特殊的四倍外推法计划更准确。我们指出,由于空间/moment解度不足而导致的标准DMD方法有可能因空间/moment解析高离性模式而导致的潜在误差。我们用离性方法展示了这种高分解法的多变式,我们用DMDMD方法展示了这个问题如何通过超常识度方法克服。