Abstract
Front Cover: In article number 2100017, Michael Wulkow and co-workers refine and apply classical and Bayesian parameter estimation for polymerization. This article aims at showing the mathematical connection of both approaches and how their combination can and should be leveraged in a closed workflow to derive a strong understanding of a model and its parameters.
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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