We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is asymptotically unbiased with respect to the theory of homogenization. Moreover, we demonstrate on a range of challenging numerical experiments that our method is accurate in extracting coarse-grained dynamics from multiscale data. In particular, the estimators we propose are more robust and require less knowledge of the full model than the standard technique of subsampling, which is widely employed in practice in this setting.
翻译:我们提出了一个基于过滤数据和移动平均数的新方法,用于从多尺度系统的观测中估计有效动态。我们在兰格文类型的半参数框架中显示,我们的方法在同质化理论方面是无差别的。此外,我们还通过一系列具有挑战性的数值实验表明,我们的方法在从多尺度数据中提取粗粒的动态方面是准确的。特别是,我们提议的估计数据更可靠,对全模型的了解程度要低于在这种环境下广泛采用的标准的子取样技术。