Learning Chemical Reactions from Simulated Data

Abstract

Catalytic chemical reactions are intricate processes that can be represented as a system of ordinary differential equations (ODEs) by deriving the rate laws for each of the species in a reaction. Different kinetic mechanisms can be associated with these systems of ODEs. A kinetic mechanism illustrates how the reaction rate depends on the kinetic constants and the concentrations of the species. Analyzing the kinetics of a reaction is crucial for understanding the behaviour of the reaction and for improving its performance. Chemists aim to automate this process by enabling extraction of the kinetics from time-series concentrations data. The problem is formulated as a least squares problem. The data used for the experiments is generated numerically using a fourth order Runge-Kutta method. Different data sampling is used to check how the distribution of the concentration data affects the final result. Three sampling options are used in the experiments: equispaced sampling, points adaptively chosen by Runge-Kutta-Fehlberg 4(5) and Chebyshev points. Apart from receiving a solution that fits the data trajectories, it is important to obtain a sparse solution. This can be achieved through the use of iterative thresholding algorithms or regularization techniques. Therefore, the sequentially thresholded least squares (STLSQ) algorithm and Lasso regularization have been utilized to extract interpretable system of ODEs from the generated data trajectories. The results obtained demonstrate that Lasso regularization is more robust against numerical errors and more frequently identifies the correct “active” components (those with non- zero coefficients on the right-hand side of the ODEs) compared to STLSQ. It has also been observed that the choice of numerical approximation for derivatives and data sampling significantly impacts the results

Date of Award	31 Dec 2023
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Kody Law (Supervisor), Stefan Guettel (Supervisor) & Igor Larrosa (Supervisor)