Dynamic Modeling of Chemical Reaction Systems with Neural Networks and Hybrid Models

Abstract

A common problem in kinetic modeling of complex chemical reactions is that a rigorous description of the reaction system, e.g., based on elementary reactions, is not possible. This is because either the reaction involves too many reactions and intermediates or the reaction mechanism is not known in sufficient detail. Alternative data-driven modeling, e.g., using neural networks, normally demands large amounts of experimental data and has poor generalization capability. In such situations a combined physical and data-driven (i.e. hybrid) model may be attractive, that utilizes the specific advantages of both approaches while avoiding their disadvantages.This paper explains the procedure of hybrid modeling of integral (i.e. time-dependent) data by using examples from chemical kinetics. The benefits of the hybrid models are described in comparison to the limiting cases of purely physical and purely data-driven models. In general, the hybrid model surpasses the purely physical and neural network models in terms of a combined interpolation-and extrapolation-range criterion. Problem DescriptionKinetic modeling of complex chemical reactions frequently suffers from a series of problems: The reaction system often involves a large number of unknown reactions and intermediates. In many cases the kinetics of the elementary reactions depend on hidden state variables, e.g., gas-phase radicals or adsorbed surface-species whose concentration cannot be quantified using conventional measurement techniques. If a reaction system includes species of extremely different lifetime, typical for radical reactions, the resulting model equations become very stiff. In this case numerical integration, even with highly efficient implicit methods, demands excessive computation time due to short integration steps. To establish rigorous physical models requires detailed information about reaction mechanisms which in many cases is associated with expensive and time-consuming experiments.Thus, alternative methods for the modeling of chemical kinetics are desirable. One promising approach lies in the use of artificial neural networks [1,2], where supervised learning is used to fit the parameters of a neural network model to a given set of measurement data by minimizing the model-data mismatch.The neural network approach avoids the problem of formulation of an appropriate reaction mechanism. However, neural networks need a very large amount of measured data. The reason is that system identification is based solely on measured data, not on a priori structural information. In particular for multidimensional systems the quantity of data required to fit a neural network model may be exceptionally high.If the training is performed on a dataset of insufficient size, the quality of the final model is usually poor. The training dataset in almost every case is still more or less accurately described. An independent dataset, i.e., not used for the adaptation of model parameters, however can be reproduced adequately only if the system dynamics have been adequate...

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