非线性薛定谔方程的参数约化模型
Parametric Reduced Models for the Nonlinear Schrödinger Equation
摘要：
导出了（散焦）非线性薛定谔方程的简化模型。特别是，我们开发的简化模型，只涉及低频模式，这些模式的噪声观测。通过对从标准Mori-Zwanzig形式主义导出的广义Langevin方程的记忆项和随机噪声分别采用有理近似和色噪声近似，得到了简化参数模型的近似解.由此产生的简化模型中的参数推断噪声观测与最近开发的集合卡尔曼滤波为基础的参数化方法。通过比较四阶矩、两次关联函数统计量和粗粒度变量的边际密度，验证了不同温度制度的预测技巧。
英文摘要：
Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parameterization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.
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