广义Langevin方程的数据驱动参数化
Data-driven parameterization of the generalized Langevin equation
摘要：
提出了一种数据驱动的方法来确定广义Langevin方程的记忆核和随机噪声。为了便于实际实现，我们参数化的核函数在拉普拉斯域的有理函数，系数直接链接到粗粒度变量的平衡统计。我们表明，这样的近似可以构造到任意高阶，由此产生的广义Langevin动力学可以嵌入到一个扩展的随机模型没有显式记忆。我们演示了如何引入随机噪声，使第二波动耗散定理是完全满足的。数值试验的结果证明了该方法的有效性。
英文摘要：
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function, with coefficients directly linked to the equilibrium statistics of the coarse-grain variables. We show that such an approximation can be constructed to arbitrarily high order and the resulting generalized Langevin dynamics can be embedded in an extended stochastic model without explicit memory. We demonstrate how to introduce the stochastic noise so that the second fluctuation-dissipation theorem is exactly satisfied. Results from several numerical tests are presented to demonstrate the effectiveness of the proposed method.
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