Model reduction of Brownian oscillators: quantification of errors and long-time behavior
Model reduction of Brownian oscillators: quantification of errors and long-time behavior
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DOI：
10.1088/1751-8121/ace948
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发表时间：
2023-04
期刊：
影响因子：
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通讯作者：
M. Colangeli;M. H. Duong;A. Muntean
中科院分区：
文献类型：
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作者：
M. Colangeli;M. H. Duong;A. Muntean
Colangeli 等人 (2022 J. Phys. A: Math. Theor. 55 505002) 最近提出了一种基于不变流形方法和波动耗散关系的带有加性噪声的随机常微分方程的模型简化过程。因此出现了一个普遍的问题，即是否可以严格量化使用简化动态代替原始动态所带来的误差。在这项工作中，我们提供了根据 Wasserstein 距离的明确公式和误差估计，无论是在要保留或从描述中消除的变量之间存在或不存在尖锐的时间尺度分离的情况下，还是在长期行为中。
A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in Colangeli et al (2022 J. Phys. A: Math. Theor. 55 505002), based on the Invariant Manifold method and on the Fluctuation–Dissipation relation. A general question thus arises as to whether one can rigorously quantify the error entailed by the use of the reduced dynamics in place of the original one. In this work we provide explicit formulae and estimates of the error in terms of the Wasserstein distance, both in the presence or in the absence of a sharp time-scale separation between the variables to be retained or eliminated from the description, as well as in the long-time behavior.