Abstract Multivariate spectroscopic data is increasingly abundant in the chemical and pharmaceutical industries. However, it is often challenging to estimate reaction kinetics directly from it. Recent advances in obtaining kinetic parameter estimates from spectroscopic data based on large-scale nonlinear programming (NLP), maximum likelihood principles, and discretization on finite elements lead to increased speed and efficiency (Chen et al., 2016). These new techniques have great potential for widespread use in parameter estimation. However they are currently limited due to their applicability to relatively small problem sizes. In this work, we extend the open-source package for estimating reaction kinetics directly from spectra or concentration data, KIPET, for use with multiple experimental datasets, or multisets (Schenk et al., 2020). Through a detailed initialization scheme and by taking advantage of large-scale nonlinear programming techniques and problem structure, we are able to solve large problems obtained from multiple experiments, simultaneously. The enhanced KIPET package can solve problems wherein multiple experiments contain different reactants and kinetic models, different dataset sizes with shared or unshared individual species’ spectra, and can obtain confidence intervals quickly based on the NLP sensitivities. In addition, we propose a new variance estimation technique based on maximum likelihood derivations for unknown covariances from two sample populations. This new variance estimation technique is compared to the previously proposed iterative-heuristics-based algorithm of Chen et al. (2016) for distinguishing between variances of the noise in model variables and in the spectral measurements. We demonstrate the new techniques on a variety of example problems, with sample code, to show the utility of the approach and its ease of use. We also include the curve-fitting problem to cases where we have concentration data given directly, and are required to estimate kinetic parameters across multiple experimental datasets.

中文翻译：

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使用 KIPET 从跨多个数据集的光谱估计方差和动力学参数

摘要 化学和制药行业中的多元光谱数据越来越丰富。然而，直接从它估计反应动力学通常具有挑战性。基于大规模非线性规划 (NLP)、最大似然原理和有限元离散化从光谱数据中获取动力学参数估计的最新进展提高了速度和效率（Chen 等，2016）。这些新技术在参数估计中具有广泛应用的巨大潜力。然而，由于它们适用于相对较小的问题规模，它们目前受到限制。在这项工作中，我们扩展了开源包，用于直接从光谱或浓度数据 KIPET 估计反应动力学，以用于多个实验数据集或多集（Schenk 等，2020）。通过详细的初始化方案并利用大规模非线性规划技术和问题结构，我们能够同时解决从多个实验中获得的大型问题。增强的 KIPET 包可以解决多个实验包含不同反应物和动力学模型、具有共享或非共享单个物种光谱的不同数据集大小的问题，并且可以根据 NLP 敏感性快速获得置信区间。此外，我们提出了一种新的方差估计技术，该技术基于来自两个样本总体的未知协方差的最大似然推导。这种新的方差估计技术与 Chen 等人先前提出的基于迭代启发式的算法进行了比较。(2016) 用于区分模型变量和频谱测量中的噪声方差。我们通过示例代码在各种示例问题上演示了新技术，以展示该方法的实用性及其易用性。我们还将曲线拟合问题包括在我们直接给出浓度数据的情况下，并且需要估计多个实验数据集的动力学参数。