Learning kinetics from non-ideal reactors by implicitly solved finite volumes and global reaction neural networks

The digitalization of chemical research and industry generates large amounts of data, offering new opportunities for developing and parameterizing kinetic models. Leveraging this data requires machine learning techniques capable of autonomously extracting kinetics from reactor datasets. Recently, neural ordinary differential equations (neural ODEs) were coupled with reactor models to learn kinetics from ideal reaction systems, such as plug-flow reactors. However, real reactor set-ups commonly feature non-idealities such as heat- and mass transfer limitations, described by partial differential equations (PDEs) or differential-algebraic equations (DAEs). Discretizing such non-ideal PDE or DAE reactor models by finite volumes yields algebraic balance equations, which are solved by numerical schemes. In this work, we propose to learn kinetics from non-ideal reactor data using these balance equations and implicit neural networks, avoiding expensive backpropagation through the numerical solution by utilizing the implicit function theorem. The approach is demonstrated for the example of a mass transfer limited flat plate reactor for the preferential catalytic oxidation of CO. We show that Global Reaction Neural Networks, embedding thermodynamic and stoichiometric prior knowledge, coupled with a discretized two-phase CSTR cascade reactor model extract intrinsic kinetics from 50 integral reactor experiments. These kinetics generalize to new reactor geometries, where kinetics obtained by neural ODEs fail. Further, the approach is robust, recovering accurate kinetics even when training data is perturbed by 10% Gaussian noise. We expect that combining neural network-based kinetics with non-ideal reactor models will broaden the scope of kinetic model discovery and improve access to accurate kinetic models.