Kinetics-constrained neural ordinary differential equations: Artificial neural network models tailored for small data to boost kinetic model development

Abstract

Artificial neural networks (ANNs) are powerful tools for solving a wide range of tasks in fundamental and applied science. However, training and building reliable ANN models requires a lot of data which so far hinders their wider application in kinetic modelling where typically only small (experimental) datasets are available. In the present work we propose a method to design ANN models for kinetic modelling that can be trained even with small data sets as are typically available. The key idea is to constrain the architecture of the ANN models by integrating kinetic and thermodynamic knowledge leading to what we call Kinetics-Constrained Neural Ordinary Differential Equations (KCNODE). The feasibility and effectiveness of the approach is first demonstrated in a numerical experiment using the catalytic hydrogenation of CO2 to methane as example. Next, we demonstrate the approach for real experimental data of a more complex reaction, the hydrogenation of CO2 to higher hydrocarbons (CO2-FT). Finally, the ANN trained for CO2-FT is used to derive an improved mechanistic model for the reverse water gas shift reaction which is a key reaction in the CO2-FT reaction network. This last step exemplifies how the opportunity to obtain reliable ANN models from small data opens new ways to approach kinetic model development.