Abstract
AbstractTwo different approaches to parameter estimation (PE) in the context of polymerization are introduced, refined, combined, and applied. The first is classical PE where one is interested in finding parameters which minimize the distance between the output of a chemical model and experimental data. The second is Bayesian PE allowing for quantifying parameter uncertainty caused by experimental measurement error and model imperfection. Based on detailed descriptions of motivation, theoretical background, and methodological aspects for both approaches, their relation are outlined. The main aim of this article is to show how the two approaches complement each other and can be used together to generate strong information gain regarding the model and its parameters. Both approaches and their interplay in application to polymerization reaction systems are illustrated. This is the first part in a two‐article series on parameter estimation for polymer reaction kinetics with a focus on theory and methodology while in the second part a more complex example will be considered.
Highlights
Introduction for exampleThis article complements these works by a combination of different approaches to the parameter estimation (PE)Parameter estimation (PE) for chemical kinetics means the process of fitting a mathematical model of the reaction process of interest to given observation data by tuning the parameters of the model
We make forward simulations with parameters with the simple model (50) which were sampled from the 3D probability distribution for the parameters and visualize the 90% percentile in each time step for these forward simulations
We have illustrated, compared, and combined two different approaches to parameter estimation: (1) the classical approach that focuses on minimizing the residual function which measures the distance between the outcome of a model and the observed data, and (2) the Bayesian approach which quantifies the uncertainty that the parameters underlie
Summary
We will concentrate on the PE problem for chemical reaction models that we are going to consider later in this article Such models can be written as systems of ordinary differential equations (ODE). The solution map F is not available in explicit form but can only be computed numerically and comes with the (often considerable) computational effort of computing the trajectory of the ODE system (1) from time 0 to time t. This is especially true for polymerization systems that are solved with respect to full chainlength distributions. As we will see later, if the evaluation of the model function is expensive, this naturally makes the use of the numerical methods we introduce expensive
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