Online Monitoring Based on Reaction Network and Kinetic Model Identification from Spectroscopic Data without a Priori knowledge of Species and Reactions

Monitoring chemically reactive complex feedstocks is crucial to limit the environmental impact by improving the process efficiency. However, the lack of enumeration of the constituents in complex feedstocks and the reaction rules governing their conversion makes reaction monitoring reliant on (i) molecular-level data from process analytical tools like spectroscopic sensors, and (ii) high physical fidelity statistical models that use the process data to infer the reaction mechanism structure and the kinetic parameters characterizing the network pathways. Given the reacting species, developing kinetic models hinges on the structure and parameters of reaction networks. The lack of prior knowledge of the network topology has prompted structure inference by virtue of parameter estimation by architecturally designing neural networks to include the law of mass action and the Arrhenius law while approximating reaction propensity as a function of the stoichiometric matrix and reaction rates, using time series concentration data of the species [1]. However, in the event that the reacting species are unknown, using structure-preserving non-negative factor decomposition of spectroscopic data that are recorded across varying operating conditions provides information on the pseudo-components. The projections of data onto the modes of the spectral channels are interpreted as pseudo-component spectra, and the projections onto the modes of the operating conditions are interpreted as the concentration of the species associated with the pseudo-component spectra, across the operating conditions, in accordance with Beer’s law [2]. The use of domain knowledge to map the peaks in the pseudo-component spectra to chemically relevant species, followed by using a graph theoretic approach of Bayesian structure learning among the pseudo-component spectra, enables hypothesizing the network topology.

We demonstrate two methods to use the projected concentration data of the pseudo-components to develop kinetic models for the system. In the first, matrix factorization is performed to decompose the rate laws into matrices representing the order of the reaction and kinetic parameters. A logarithmic transformation allows the rate law to be represented as a linear combination of concentration profiles and temperatures with each term being weighted by the order of the reaction and kinetic parameters, respectively. The concentration profiles across various temperatures are stacked to form a concentration matrix which is then numerically differentiated to obtain the rate of transformation of each species. A simultaneous factorization of the rate matrix across all temperatures is performed to guarantee the consistency of reaction order across all process conditions. An optimal factorization is achieved by minimizing the L₂ norm of the difference between the actual rates and the linear combination of the decompositions. The initial guess of the parameters is obtained through the Sparse Identification of Non-linear Dynamics (SINDy) framework for LASSO regression with a library matrix consisting of an ensemble of simple rate laws. This routine further incorporates the topology of the predetermined reaction network (obtained by Bayesian structure learning). The decomposition begins from the root node of the graph only incorporating the terms corresponding to that species. As the algorithm traverses the graph, the decomposition for subsequent nodes involves the concentration terms of the parent nodes and in some cases the child node (in the case of a reversible reaction). An alternating least squares approach is used in such cases to simultaneously produce decompositions for the parent and the child nodes, and the process is repeated for each species (i.e., pseudo-component). In contrast to a SINDy-based model identification, this direct factorization does not suffer from an inherent bias established by the type of features chosen in the library matrix, and honors the topology of the reaction network.

In the second method, we demonstrate the use of the projected concentration data of the pseudo-components for the development of a kinetically informed neural network architecture constrained by the adjacency matrix of the network topology from Bayesian networks to functionally approximate the reaction propensity. The logarithm of the projected concentrations are the inputs to a simple feedforward neural network, with the objective of predicting the time rate of change of the species concentration, such that the squared differences of these predictions from the numerically ascertained reaction rates from the concentration projection data is minimized, while being regularized by the network adjacency matrix. The weights of the first layer represent the reaction orders, followed by an exponential activation in the hidden layer comprising as many neurons as the number of reaction pathways identified by the Bayesian networks, and finally, the weights of the output layer correspond to the stoichiometric coefficients. Both methods presented are shown to achieve online reaction monitoring of complex chemical systems in the absence of prior knowledge of the underlying species and their reaction mechanisms, which has not been demonstrated before for complex reacting systems. Results are presented for biomass conversion and partial upgrading of bitumen.

Keywords: Chemical reaction neural networks, reaction hypothesis, latent factor decomposition, Bayesian networks, constrained kinetic models, sparse identification, reaction monitoring

References:

[1] W. Ji and S. Deng, “Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network,” J. Phys. Chem. A, vol. 125, no. 4, pp. 1082–1092, 2021, doi: 10.1021/acs.jpca.0c09316.

[2] A. Puliyanda, K. Sivaramakrishnan, Z. Li, A. De Klerk, and V. Prasad, “Data fusion by joint non-negative matrix factorization for hypothesizing pseudo-chemistry using Bayesian networks,” React. Chem. Eng., vol. 5, no. 9, pp. 1719–1737, 2020, doi: 10.1039/d0re00147c.