[Paper Review] The Automated Discovery of Kinetic Rate Models -- Methodological Frameworks

Miguel Ángel de Carvalho Servia, Ilya Orson Sandoval+5 more|arXiv (Cornell University)|Jan 26, 2023

Machine Learning in Materials Science4 citations

TL;DR

This paper proposes ADoK-S and ADoK-W, two automated frameworks for discovering catalytic kinetic rate models using symbolic regression with rigorous model selection via information criteria. By combining genetic programming for model generation and sequential optimization with MBDoE-guided experiments, the frameworks successfully recover true kinetic mechanisms from limited, noisy data across three complex case studies, demonstrating robustness and scalability in chemical reaction engineering applications.

ABSTRACT

The industrialization of catalytic processes requires reliable kinetic models for their design, optimization and control. Mechanistic models require significant domain knowledge, while data-driven and hybrid models lack interpretability. Automated knowledge discovery methods, such as ALAMO (Automated Learning of Algebraic Models for Optimization), SINDy (Sparse Identification of Nonlinear Dynamics), and genetic programming, have gained popularity but suffer from limitations such as needing model structure assumptions, exhibiting poor scalability, and displaying sensitivity to noise. To overcome these challenges, we propose two methodological frameworks, ADoK-S and ADoK-W (Automated Discovery of Kinetic rate models using a Strong/Weak formulation of symbolic regression), for the automated generation of catalytic kinetic models using a robust criterion for model selection. We leverage genetic programming for model generation and a sequential optimization routine for model refinement. The frameworks are tested against three case studies of increasing complexity, demonstrating their ability to retrieve the underlying kinetic rate model with limited noisy data from the catalytic systems, showcasing their potential for chemical reaction engineering applications.

Motivation & Objective

• To address the limitations of existing automated knowledge discovery methods in kinetic model generation, such as structural assumptions, poor scalability, and sensitivity to noise.
• To develop a robust, generalizable framework for automated discovery of interpretable kinetic rate models without requiring prior mechanistic knowledge.
• To integrate rigorous model selection using information criteria (AIC/BIC) to ensure statistical validity and transparency in model ranking.
• To enhance data efficiency by using MBDoE (Multi-Block Bayesian Design of Experiments) to guide sequential experimentation and improve model accuracy iteratively.
• To demonstrate the framework's capability on increasingly complex catalytic systems, including isomerization, N₂O decomposition, and toluene hydrodealkylation.

Proposed method

• Employ genetic programming to explore a vast space of candidate symbolic expressions for kinetic rate laws, enabling flexible, data-driven model generation.
• Apply a sequential optimization routine to refine model parameters using nonlinear least-squares fitting on concentration profiles from experimental data.
• Utilize AIC and BIC as information criteria for objective, transparent model selection, favoring models with optimal balance between fit and complexity.
• Integrate MBDoE to strategically design new experiments based on uncertainty in current model predictions, improving data efficiency and convergence.
• Use strong (ADoK-S) and weak (ADoK-W) formulations of symbolic regression to enhance robustness: ADoK-S directly models rate expressions, while ADoK-W uses integrated concentration profiles.
• Concatenate new experimental data after each iteration to iteratively improve model discovery, ensuring convergence toward the true kinetic mechanism.

Experimental results

Research questions

• RQ1 Can automated symbolic regression frameworks discover the true underlying kinetic rate law from limited, noisy experimental data without prior mechanistic assumptions?
• RQ2 How does the integration of information criteria (AIC/BIC) improve model selection robustness compared to heuristic or non-transparent criteria in kinetic model discovery?
• RQ3 To what extent can MBDoE-guided sequential experimentation enhance the accuracy and convergence of automated kinetic model discovery?
• RQ4 How do the strong and weak formulations in ADoK-S and ADoK-W differ in performance and robustness across systems of increasing complexity?
• RQ5 Can the proposed frameworks recover interpretable, physically meaningful kinetic expressions that match the ground-truth rate laws in real catalytic systems?

Key findings

• ADoK-S successfully recovered the true kinetic rate model for the hydrodealkylation of toluene after only five initial experiments, with a structurally identical and parameter-similar model: $\hat{r}^{*} = \frac{1.124C_{T}C_{H}}{1+4.932C_{B}+2.928C_{T}}$.
• For the isomerization reaction, ADoK-W rediscovered the ground-truth rate model after six experiments, achieving $\hat{r}^{*} = \frac{9.998C_{A}-4.496C_{B}+0.386}{6.038C_{A}+2.137C_{B}+7.892}$, with only a minor, negligible extra parameter.
• In the N₂O decomposition case, ADoK-W uncovered the correct model structure $\hat{r}^{*} = \frac{1.584C_{N_{2}O}^{2}}{1+3.798C_{N_{2}O}}$ after seven experiments, demonstrating recovery even under high noise and complex dynamics.
• The frameworks showed resilience to noisy data and poor initial data quality, with model selection via AIC/BIC effectively filtering spurious candidates.
• The integration of MBDoE significantly improved data efficiency, enabling model discovery with fewer experiments than would be required by random or uniform sampling.
• All discovered models were structurally and parametrically close to the true kinetic expressions, confirming the methodological robustness and interpretability of the approach.