Benjamin C. Koenig

Benjamin C. Koenig, Suyong Kim, Sili Deng

Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a neural ordinary differential equation (ODE) framework, generalizing their use to the time-dependent and temporal grid-sensitive cases often seen in dynamical systems and scientific machine learning applications. The proposed KAN-ODEs retain the flexible dynamical system modeling framework of Neural ODEs while leveraging the many benefits of KANs compared to MLPs, including higher accuracy and faster neural scaling, stronger interpretability and generalizability, and lower parameter counts. First, we quantitatively demonstrated these improvements in a comprehensive study of the classical Lotka-Volterra predator-prey model. We then showcased the KAN-ODE framework's ability to learn symbolic source terms and complete solution profiles in higher-complexity and data-lean scenarios including wave propagation and shock formation, the complex Schrödinger equation, and the Allen-Cahn phase separation equation. The successful training of KAN-ODEs, and their improved performance compared to traditional Neural ODEs, implies significant potential in leveraging this novel network architecture in myriad scientific machine learning applications for discovering hidden physics and predicting dynamic evolution.

Benjamin C. Koenig, Sili Deng

Thermal runaway in lithium-ion batteries is strongly influenced by the state of charge (SOC). Existing predictive models typically infer scalar kinetic parameters at a full SOC or a few discrete SOC levels, preventing them from capturing the continuous SOC dependence that governs exothermic behavior during abuse conditions. To address this, we apply the Kolmogorov-Arnold Chemical Reaction Neural Network (KA-CRNN) framework to learn continuous and realistic SOC-dependent exothermic cathode-electrolyte interactions. We apply a physics-encoded KA-CRNN to learn SOC-dependent kinetic parameters for cathode-electrolyte decomposition directly from differential scanning calorimetry (DSC) data. A mechanistically informed reaction pathway is embedded into the network architecture, enabling the activation energies, pre-exponential factors, enthalpies, and related parameters to be represented as continuous and fully interpretable functions of the SOC. The framework is demonstrated for NCA, NM, and NMA cathodes, yielding models that reproduce DSC heat-release features across all SOCs and provide interpretable insight into SOC-dependent oxygen-release and phase-transformation mechanisms. This approach establishes a foundation for extending kinetic parameter dependencies to additional environmental and electrochemical variables, supporting more accurate and interpretable thermal-runaway prediction and monitoring.

Benjamin C. Koenig, Sili Deng

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.

Benjamin C. Koenig, Suyong Kim, Sili Deng

The recently proposed Kolmogorov-Arnold network (KAN) is a promising alternative to multi-layer perceptrons (MLPs) for data-driven modeling. While original KAN layers were only capable of representing the addition operator, the recently-proposed MultKAN layer combines addition and multiplication subnodes in an effort to improve representation performance. Here, we find that MultKAN layers suffer from a few key drawbacks including limited applicability in output layers, bulky parameterizations with extraneous activations, and the inclusion of complex hyperparameters. To address these issues, we propose LeanKANs, a direct and modular replacement for MultKAN and traditional AddKAN layers. LeanKANs address these three drawbacks of MultKAN through general applicability as output layers, significantly reduced parameter counts for a given network structure, and a smaller set of hyperparameters. As a one-to-one layer replacement for standard AddKAN and MultKAN layers, LeanKAN is able to provide these benefits to traditional KAN learning problems as well as augmented KAN structures in which it serves as the backbone, such as KAN Ordinary Differential Equations (KAN-ODEs) or Deep Operator KANs (DeepOKAN). We demonstrate LeanKAN's simplicity and efficiency in a series of demonstrations carried out across a standard KAN toy problem as well as ordinary and partial differential equations learned via KAN-ODEs, where we find that its sparser parameterization and compact structure serve to increase its expressivity and learning capability, leading it to outperform similar and even much larger MultKANs in various tasks.

Benjamin C. Koenig, Suyong Kim, Sili Deng

Efficient chemical kinetic model inference and application in combustion are challenging due to large ODE systems and widely separated time scales. Machine learning techniques have been proposed to streamline these models, though strong nonlinearity and numerical stiffness combined with noisy data sources make their application challenging. Here, we introduce ChemKANs, a novel neural network framework with applications both in model inference and simulation acceleration for combustion chemistry. ChemKAN's novel structure augments the generic Kolmogorov Arnold Network Ordinary Differential Equations (KAN-ODEs) with knowledge of the information flow through the relevant kinetic and thermodynamic laws. This chemistry-specific structure combined with the expressivity and rapid neural scaling of the underlying KAN-ODE algorithm instills in ChemKANs a strong inductive bias, streamlined training, and higher accuracy predictions compared to standard benchmarks, while facilitating parameter sparsity through shared information across all inputs and outputs. In a model inference investigation, we benchmark the robustness of ChemKANs to sparse data containing up to 15% added noise, and superfluously large network parameterizations. We find that ChemKANs exhibit no overfitting or model degradation in any of these training cases, demonstrating significant resilience to common deep learning failure modes. Next, we find that a remarkably parameter-lean ChemKAN (344 parameters) can accurately represent hydrogen combustion chemistry, providing a 2x acceleration over the detailed chemistry in a solver that is generalizable to larger-scale turbulent flow simulations. These demonstrations indicate the potential for ChemKANs as robust, expressive, and efficient tools for model inference and simulation acceleration for combustion physics and chemical kinetics.