Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.

中文翻译：

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机械模型中的统计推断：时间扭曲可改善梯度匹配。

非线性微分方程的力学模型的推论是当前计算统计中的一个具有挑战性的问题。由于在迭代参数自适应方案的每个步骤中对微分方程进行数值求解的计算成本较高，因此基于梯度匹配的近似方法变得很流行。但是，这些方法严重依赖于函数插值的平滑方案。本文采用了来自多种学习的思想，并证明了一种旨在使内在长度尺度均匀化的时间扭曲方法可以显着提高参数估计的准确性。我们证明了该方案对两个动态系统的噪声数据的有效性，该系统具有周期性极限周期，生物通路和软组织力学的应用。