Title:
Neural-network representations of chemical kinetics
Neural-network representations of chemical kinetics
Author(s)
Sabenca Gusmao, Gabriel
Advisor(s)
Medford, Andrew J.
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Abstract
High-fidelity microkinetic models (MKMs) have provided a framework for understanding and mathematically representing the elementary processes underpinning catalytic reactions in terms of differential equations. Computational chemistry methods, such as density functional theory, have enabled the estimation of the thermochemistry of elementary reactions on different catalytic materials from first-principles. MKMs constructed around computational chemistry methods have proven useful in determining trends in catalytic activity across different materials. Nevertheless, there are still challenges to overcome: (i) the inclusion of lateral interactions and solvation effects in models leads to over-parameterization, making the mean-field approximation useless and approximating MKMs to kinetic Monte-Carlo; (ii) uncertainties in the structure of the active site and the detailed mechanism, and (iii) non-standardization in the reported thermochemistry models.
In this thesis, we introduce a general and unifying algebraic framework that uses singular value decomposition to assess the connectivity of complex reaction networks. Such a framework addresses the standardization issue by leveraging the use of thermochemical data from multiple sources, allowing them to be re-referenced or combined in extended reaction mechanisms. It also generalizes the construction of descriptor-based models by providing a means to quantify the explained variance by each descriptor. With this general algebraic representation of MKM thermochemistry, we set our focus on creating methods to bridge information from transient experiments to high-fidelity MKMs.
Physics-informed neural networks (PINNs) have proven to be a suitable mathematical scaffold for solving inverse ordinary (ODE) and partial differential equations (PDE). In this work, we devise an application of the PINNs formulation designed to address inverse kinetics problems, which we call Kinetics-Informed Neural Networks (KINNs). It consists of soft-constrained multi-objective optimization problems that include a hyperparameter that controls the variance between adhering to physical laws and interpolating observed data. We further bridge the statistical formulation of the error probability density in inverse PINNs to frame it in terms of maximum-likelihood estimators (MLE), which allows explicit error propagation from interpolation to the physical model space through Taylor expansion, thereby eliminating the need for hyperparameter tuning. We explore its application to high-dimensional coupled ODEs constrained by differential algebraic equations that are common in transient chemical and biological kinetics. Furthermore, we show that singular-value decomposition (SVD) of the ODE coupling matrices (reaction stoichiometry matrices) provides reduced uncorrelated subspaces in which PINNs solutions can be represented and over which residuals can be projected. Finally, SVD bases serve as preconditioners for the inversion of covariance matrices in this hyperparameter-free robust application of MLE to KINNs, in robust-KINNs (rKINNs).
Our exploration extends to applying rKINNs to high-fidelity MKMs constructed from an amalgamation of literature-reported DFT energies relying on the developed unified algebraic thermochemistry framework. We embed domain knowledge into the singular computational perturbation (CSP) approach to satisfy MKM constitutional constraints and generate synthetic data by solving the stiff forward differential equations associated with transient reactor models of laboratory-scale. In this endeavor, we probe the limits of realistic chemical dynamics recoverability, using the ab-initio predicted timescales of the RWGS MKM as a case study.
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Date Issued
2023-12-12
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Text
Resource Subtype
Dissertation