Deactivation Neural Ordinary Differential Equation (deactNODE)─Learning Deactivation Kinetics from Integral Data

Abstract Catalyst deactivation critically affects the long-term reactor performance. Thus, the development and parametrization of accurate models to predict the effect of operation conditions is crucial for reactor design. Current models are limited by power-law frameworks or lack the flexibility to be used in reactor models. In this work, the application of artificial neural networks (aNNs) to learn deactivation kinetics is demonstrated and critically evaluated against state-of-the-art power law models. Hence, a rate-based deactivation model is proposed in which an unconstrained aNN learns the intrinsic activity gradient as a function of the catalyst state and operation conditions. The model is trained on activity-time data using an integral strategy based on the neural ordinary differential equation method, enabling direct use of experimentally accessible quantities. Using simulated deactivation experiments, a systematic hyperparameter study is conducted to identify suitable network architectures, and the NODE training strategy is demonstrated. The model accurately predicts temperature-dependent deactivation data and shows robust interpolation to unseen conditions, even with small data sets. Application to long-term CO methanation experiments over a Ni-based catalyst demonstrates excellent agreement with experimental activity profiles, capturing regime changes and complex temperature effects. A comparison to a power-law deactivation model yields similarly good best fits with the aNN showing greater robustness to random initialization. A cross-validation study underlines the strong interpolation capability of the aNN, whereas both power-law and aNN models show limitations for extrapolation, as expected for empirical models. Overall, the aNN-based model provides an accurate, flexible, and robust alternative to the classical power-law deactivation models.