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Kolmogorov-Arnold Chemical Reaction Neural Networks for learning pressure-dependent kinetic rate laws

Benjamin C. Koenig, Sili Deng

TL;DR

The paper addresses the limitation that standard CRNNs cannot capture pressure-dependent chemical kinetics, a gap that hampers accurate modeling in combustion and related systems. It introduces KA-CRNN, which couples a physics-informed CRNN backbone with univariate Kolmogorov-Arnold activations to render each kinetic parameter (Ea, A, b) a learnable function of pressure while preserving Arrhenius and mass-action structure. The authors demonstrate a proof-of-concept on CH$_3$ recombination with Troe falloff, showing that KA-CRNN can accurately reconstruct pressure- and temperature-dependent rates using a very small parameter set and outperforming PLOG interpolations and MLP baselines. The work establishes a path toward data-driven, interpretable discovery of extended kinetic behaviors under external forcings, with broad applicability beyond combustion and potential for symbolic interpretation of learned rate dependencies.

Abstract

Chemical Reaction Neural Networks (CRNNs) have emerged as an interpretable machine learning framework for discovering reaction kinetics directly from data, while strictly adhering to the Arrhenius and mass action laws. However, standard CRNNs cannot represent pressure-dependent rate behavior, which is critical in many combustion and chemical systems and typically requires empirical formulations such as Troe or PLOG. Here, we develop Kolmogorov-Arnold Chemical Reaction Neural Networks (KA-CRNNs) that generalize CRNNs by modeling each kinetic parameter as a learnable function of system pressure using Kolmogorov-Arnold activations. This structure maintains full interpretability and physical consistency while enabling assumption-free inference of pressure effects directly from data. A proof-of-concept study on the CH3 recombination reaction demonstrates that KA-CRNNs accurately reproduce pressure-dependent kinetics across a range of temperatures and pressures, outperforming conventional interpolative models. The framework establishes a foundation for data-driven discovery of extended kinetic behaviors in complex reacting systems, advancing interpretable and physics-consistent approaches for chemical model inference.

Kolmogorov-Arnold Chemical Reaction Neural Networks for learning pressure-dependent kinetic rate laws

TL;DR

The paper addresses the limitation that standard CRNNs cannot capture pressure-dependent chemical kinetics, a gap that hampers accurate modeling in combustion and related systems. It introduces KA-CRNN, which couples a physics-informed CRNN backbone with univariate Kolmogorov-Arnold activations to render each kinetic parameter (Ea, A, b) a learnable function of pressure while preserving Arrhenius and mass-action structure. The authors demonstrate a proof-of-concept on CH recombination with Troe falloff, showing that KA-CRNN can accurately reconstruct pressure- and temperature-dependent rates using a very small parameter set and outperforming PLOG interpolations and MLP baselines. The work establishes a path toward data-driven, interpretable discovery of extended kinetic behaviors under external forcings, with broad applicability beyond combustion and potential for symbolic interpretation of learned rate dependencies.

Abstract

Chemical Reaction Neural Networks (CRNNs) have emerged as an interpretable machine learning framework for discovering reaction kinetics directly from data, while strictly adhering to the Arrhenius and mass action laws. However, standard CRNNs cannot represent pressure-dependent rate behavior, which is critical in many combustion and chemical systems and typically requires empirical formulations such as Troe or PLOG. Here, we develop Kolmogorov-Arnold Chemical Reaction Neural Networks (KA-CRNNs) that generalize CRNNs by modeling each kinetic parameter as a learnable function of system pressure using Kolmogorov-Arnold activations. This structure maintains full interpretability and physical consistency while enabling assumption-free inference of pressure effects directly from data. A proof-of-concept study on the CH3 recombination reaction demonstrates that KA-CRNNs accurately reproduce pressure-dependent kinetics across a range of temperatures and pressures, outperforming conventional interpolative models. The framework establishes a foundation for data-driven discovery of extended kinetic behaviors in complex reacting systems, advancing interpretable and physics-consistent approaches for chemical model inference.

Paper Structure

This paper contains 6 sections, 6 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Methodology
  3. Kolmogorov-Arnold Chemical Reaction Neural Networks
  4. Pressure-sensitive reaction model
  5. Results and Discussion
  6. Conclusions

Figures (4)

  • Figure 1: KA-CRNN model with learnable activation parameters that respond to the system pressure.
  • Figure 2: KA-CRNN reconstructions of all 27 datasets, using just three pressure-sensitive kinetic parameters. Individual profiles are evaluated at [M] = $10^{-i}$ mol/cm$^3$, $i=2:10$.
  • Figure 3: KAN activations and individual basis functions of the three learned kinetic parameters. Nine network parameters are used for each activation (27 total KA-CRNN parameters).
  • Figure 4: KA-CRNN reaction rates. Synthetic data from the Troe model, with comparison against PLOG interpolation. Training is at discrete [M] values, with continuous testing at unseen intermediate values. Further testing is at fully unseen temperatures ([900K, 1100K]).