Second-order linear differential equations can be used as models for regulation since under a range of parameter values they can account for a return to equilibrium as well as potential oscillations in regulated variables. One method that can estimate parameters of these equations from intensive time series data is the method of Latent Differential Equations (LDE). However, the LDE method can exhibit bias in its parameters if the dimension of the time delay embedding and thus the width of the convolution kernel is not chosen wisely. This article presents a simulation study showing that a constrained fourth-order Latent Differential Equation (FOLDE) model for the second-order system almost completely eliminates bias as long as the width of the convolution kernel is less than two-thirds the period of oscillations in the data. The FOLDE model adds two degrees of freedom over the standard LDE model but significantly improves model fit.

中文翻译：

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受约束的四阶潜在微分方程减少了阻尼线性振荡器模型的参数估计偏差

二阶线性微分方程可以用作调节模型，因为在一定范围的参数值下，它们可以解释平衡的回归以及调节变量的潜在振荡。可以从密集的时间序列数据中估计这些方程参数的一种方法是潜在微分方程 (LDE) 方法。然而，如果时间延迟嵌入的维度和卷积核的宽度没有明智地选择，LDE 方法可能会在其参数中表现出偏差。本文提出的仿真研究表明，只要卷积核的宽度小于振荡周期的三分之二，二阶系统的约束四阶潜在微分方程 (FOLDE) 模型几乎可以完全消除偏差。数据。