Linear response based parameter estimation in the presence of model error
Linear response based parameter estimation in the presence of model error
复制标题
DOI：
10.1016/j.jcp.2021.110112
复制
发表时间：
2021-02-03
影响因子：
4.1
通讯作者：
Li，Xiantao
中科院分区：
文献类型：
--
作者：
Zhang，He;Harlim，John;Li，Xiantao
最近，我们提出了一种基于线性响应统计的随机动力学参数估计方法。该方法基于非线性最小二乘问题，该问题考虑了源于波动耗散理论的响应特性。在本文中，我们将讨论在出现模型错误时出现的一个重要问题。特别是，当平衡密度函数是高维的非高斯函数时，在某些情况下，是未知的，线性响应统计是不可访问的。我们表明，这个问题可以通过将不完善的模型拟合到适当的边际线性响应统计量来解决，这些统计量可以使用可用的数据和参数或非参数模型来近似。参数估计方法的有效性在具有非均匀温度分布的分子动力学模型（朗之万动力学）和显示时空混沌的PDE（非朗之万动力学）的背景下得到了证明，其中建模误差是由于粗粒化造成的，其中模型误差是由于严重的光谱截断。在这些例子中，我们展示了不完全模型，即使用所提出的格式估计参数的朗之万方程如何预测潜在动力学的非线性响应统计量。
Recently, we proposed a method to estimate parameters of stochastic dynamics based on the linear response statistics. The method rests upon a nonlinear least-squares problem that takes into account the response properties that stem from the Fluctuation-Dissipation Theory. In this article, we address an important issue that arises in the presence of model error. In particular, when the equilibrium density function is high dimensional and non-Gaussian, and in some cases, is unknown, the linear response statistics are inaccessible. We show that this issue can be resolved by fitting the imperfect model to appropriatemarginal linear response statisticsthat can be approximated using the available data and parametric or nonparametric models. The effectiveness of the parameter estimation approach is demonstrated in the context of molecular dynamical models (Langevin dynamics) with a non-uniform temperature profile, where the modeling error is due to coarse-graining, and a PDE (non-Langevin dynamics) that exhibits spatiotemporal chaos, where the model error arises from a severe spectral truncation. In these examples, we show how the imperfect models, the Langevin equation with parameters estimated using the proposed scheme, can predict the nonlinear response statistics of the underlying dynamics underadmissible external disturbances.