Fitting micro-kinetic models to transient kinetics of temporal analysis of product reactors using kinetics-informed neural networks

TL;DR

The paper tackles the challenge of extracting physically interpretable kinetics from TAP transient data, especially for large multi-pulse datasets. It introduces kinetics-informed neural networks (KINNs) that solve MKM-constrained ODEs while fitting TAP data, enabling simultaneous state interpolation and kinetic parameter inference. The work demonstrates three case studies—ideal single-pulse, ideal multi-pulse, and practical multi-pulse with noise—showing improved noise tolerance over DAEs and the ability to interpolate unseen pulses; it also addresses partial thin-zone information via uptake constraints and the Y-procedure. The approach offers a scalable, robust alternative for TAP analysis with potential to integrate thermodynamics and spectroscopic constraints, facilitating more reliable kinetic insight for complex catalytic systems.

Abstract

The temporal analysis of products (TAP) technique produces extensive transient kinetic data sets, but it is challenging to translate the large quantity of raw data into physically interpretable kinetic models, largely due to the computational scaling of existing numerical methods for fitting TAP data. In this work, we utilize kinetics-informed neural networks (KINNs), which are artificial feedforward neural networks designed to solve ordinary differential equations constrained by micro-kinetic models, to model the TAP data. We demonstrate that, under the assumption that all concentrations are known in the thin catalyst zone, KINNs can simultaneously fit the transient data, retrieve the kinetic model parameters, and interpolate unseen pulse behavior for multi-pulse experiments. We further demonstrate that, by modifying the loss function, KINNs maintain these capabilities even when precise thin-zone information is unavailable, as would be the case with real experimental TAP data. We also compare the approach to existing optimization techniques, which reveals improved noise tolerance and performance in extracting kinetic parameters. The KINNs approach offers an efficient alternative for TAP analysis and can assist in interpreting transient kinetics in complex systems over long timescales.

Figures (7)

• Figure 1: Workflow of modeling TAP data with KINNs. The raw outlet response is processed to obtain thin zone concentration and flux that are fed into constructed KINN model. The obtained KINN parameters can be used to interpolate single or multi-pulse data, and the kinetic parameters can be used directly in kinetic models or serve as an initial guesses for refinement using PDE tools like TAPSolver.
• Figure 2: KINN optimization of single-pulse CO oxidation under minimization of cost function $J$ in Eq. \ref{['eqn:loss_fn']} for (a) concentrations, where circles represent target values and dashed lines represent predicted values, and (b) a parity plot of rates extracted from the KINN model and predicted from the kinetic model.
• Figure 3: Ground truth TAP curve (solid line) and TAP curve obtained from solving ODEs with kinetic parameters extracted from the KINN (dash-dotted line) and the ground truth parameters (dotted line).
• Figure 4: KINN's predicted scaled concentration (dashed line) and target ground truth value (dot) for the training set (pulse 0, 2) and interpolating to the testing set (pulse 3, 6) for gas species (top) and adspecies (bottom).
• Figure 5: Training (top) and testing (bottom) performance for practical multi-pulse case under minimization of Eq.\ref{['eqn:loss_fn_uptake']}.