Sili Deng

Turbulent combustion simulations are crucial for many scientific and engineering systems. However, the high cost to fully resolve the complex multiscale and multiphysics behavior makes direct simulation typically infeasible. The equivalent reactor network (ERN) approach attempts to improve computational efficiency by replacing a multidimensional turbulent simulation with a series of much cheaper 0-D and 1-D chemical reactors, providing a surrogate model that retains detailed chemistry at the cost of simplified flow physics. However, their development remains a challenge, often requiring either expert analysis, or automated approaches that sacrifice accuracy. In this work, we develop an automated machine-learning-assisted framework for constructing ERNs of the Sandia-D turbulent methane/air flame. Principal component analysis is first used to reduce high-dimensional thermochemical computational fluid dynamics (CFD) data to a low-dimensional latent space, where k-means clustering identifies physically interpretable flame regions used to initialize a reactor-network graph. This initialization is then refined using finite-difference gradient descent wrapped around non-differentiable Cantera reactor simulations. Across 30 RANS simulations spanning a range of pilot temperatures and inlet methane compositions, the optimized 7-reactor ERN achieves a maximum-temperature $R^2$ score of 0.7945 while preserving a $\sim6000\times$ speedup over the CFD solver. Outlet CO prediction remains more challenging, with a final $R^2$ score of $-0.4183$, but improves substantially from the unoptimized clustering initialization. These results show that unsupervised thermochemical feature extraction can provide effective physics-informed initializations for ERN construction, while gradient-based refinement can significantly improve predictive accuracy without manual reactor-network design.

Turbulent combustion simulations are crucial for many scientific and engineering systems. However, the high cost to fully resolve the complex multiscale and multiphysics behavior makes direct simulation typically infeasible. The equivalent reactor network (ERN) approach attempts to improve computational efficiency by replacing a multidimensional turbulent simulation with a series of much cheaper 0-D and 1-D chemical reactors, providing a surrogate model that retains detailed chemistry at the cost of simplified flow physics. However, their development remains a challenge, often requiring either expert analysis, or automated approaches that sacrifice accuracy. In this work, we develop an automated machine-learning-assisted framework for constructing ERNs of the Sandia-D turbulent methane/air flame. Principal component analysis is first used to reduce high-dimensional thermochemical computational fluid dynamics (CFD) data to a low-dimensional latent space, where k-means clustering identifies physically interpretable flame regions used to initialize a reactor-network graph. This initialization is then refined using finite-difference gradient descent wrapped around non-differentiable Cantera reactor simulations. Across 30 RANS simulations spanning a range of pilot temperatures and inlet methane compositions, the optimized 7-reactor ERN achieves a maximum-temperature $R^2$ score of 0.7945 while preserving a $\sim6000\times$ speedup over the CFD solver. Outlet CO prediction remains more challenging, with a final $R^2$ score of $-0.4183$, but improves substantially from the unoptimized clustering initialization. These results show that unsupervised thermochemical feature extraction can provide effective physics-informed initializations for ERN construction, while gradient-based refinement can significantly improve predictive accuracy without manual reactor-network design.

This work presents a reduced mechanism for NH3/H2/air combustion derived directly from a high-fidelity, firstprinciples-based parent model [1] without empirical modification of kinetic or thermochemical parameters. Starting from a 53-species detailed mechanism, an iterative reduction strategy was used to obtain a 23-species reduced mechanism while preserving the parent chemistry. The reduced mechanism was assessed against a broad validation suite including ignition delay times, laminar burning velocities, jet-stirred reactor species profiles, plug flow reactor species evolution, extinction strain rates, and turbulent computational fluid dynamics (CFD) fidelity tests. Across the canonical validation configurations, the reduced mechanism’s results closely matched those of the detailed parent mechanism, indicating that the dominant ignition, flame-propagation, intermediate-species, and NOxformation pathways are preserved. Relative to representative reduced mechanisms in the literature, the present mechanism provided consistently balanced performance over pure NH3 and NH3/H2 conditions, while avoiding the empirical retuning commonly used in compact ammonia-fuel chemistry. In a CFD simulation of a turbulent partially premixed NH3/H2/N2-air jet flame, the reduced mechanism reproduced the detailed-mechanism predictions of temperature, NH, and NO with negligible visible loss of fidelity while reducing computational cost by approximately a factor of five. The resulting mechanism provides a physically grounded, CFD-practical chemistry model for predictive simulations of ammonia/hydrogen combustion across wide ranges of conditions.

Nickel-rich (Ni-rich) layered oxides offer high specific capacities but suffer from rapid degradation during prolonged cycling, with anisotropic lattice deformation being a widely discussed cause. Embedding strain-buffering phases within the cathode structure mitigates this degradation by suppressing adverse volumetric changes. Here, a flame-assisted spray pyrolysis method is developed to introduce interwoven rocksalt-like and spinel-like phases into layered structured Li(Ni 0.8 Co 0.1 Mn 0.1 )O 2 (NCM811) using nanoparticle-laden suspension precursors containing nickel hydroxide. Electrochemical measurements and in situ X-ray diffraction demonstrated enhanced structural stability during cycling. Atomic-resolution HAADF-STEM imaging reveals that the secondary phases form coherent, interwoven nanoscale domains within the primary layered matrix. This rapid and scalable synthesis approach enables heterogeneous phase engineering in Ni-rich cathodes, offering a viable route toward improved cycling stability. The results underscore the potential of nanoparticle-seeded precursors for tailoring the phase architecture in energy materials.

Flame tomography is a compelling approach for extracting large amounts of data from experiments via 3-D thermochemical reconstruction. Recent efforts employing neural-network flame representations have suggested improved reconstruction quality compared with classical tomography approaches, but a rigorous quantitative comparison with the same algorithm using a voxel-grid representation has not been conducted. Here, we compare a classical voxel-grid representation with varying regularizers to a continuous neural representation for tomographic reconstruction of a simulated pool fire. The representations are constructed to give temperature and composition as a function of location, and a subsequent ray-tracing step is used to solve the radiative transfer equation to determine the spectral intensity incident on hyperspectral infrared cameras, which is then convolved with an instrument lineshape function. We demonstrate that the voxel-grid approach with a total-variation regularizer reproduces the ground-truth synthetic flame with the highest accuracy for reduced memory intensity and runtime. Future work will explore more representations and under experimental configurations.

Flame tomography is a compelling approach for extracting large amounts of data from experiments via 3-D thermochemical reconstruction. Recent efforts employing neural-network flame representations have suggested improved reconstruction quality compared with classical tomography approaches, but a rigorous quantitative comparison with the same algorithm using a voxel-grid representation has not been conducted. Here, we compare a classical voxel-grid representation with varying regularizers to a continuous neural representation for tomographic reconstruction of a simulated pool fire. The representations are constructed to give temperature and composition as a function of location, and a subsequent ray-tracing step is used to solve the radiative transfer equation to determine the spectral intensity incident on hyperspectral infrared cameras, which is then convolved with an instrument lineshape function. We demonstrate that the voxel-grid approach with a total-variation regularizer reproduces the ground-truth synthetic flame with the highest accuracy for reduced memory intensity and runtime. Future work will explore more representations and under experimental configurations.

Digital twins of complex physical systems are expected to infer unobserved states from sparse measurements and predict their evolution in time, yet these two functions are typically treated as separate tasks. Here we present GLU, a Global-Local-Uncertainty framework that formulates sparse reconstruction and dynamic forecasting as a unified state-representation problem and introduces a structured latent assembly to both tasks. The central idea is to build a structured latent state that combines a global summary of system-level organization, local tokens anchored to available measurements, and an uncertainty-driven importance field that weights observations according to the physical informativeness. For reconstruction, GLU uses importance-aware adaptive neighborhood selection to retrieve locally relevant information while preserving global consistency and allowing flexible query resolution on arbitrary geometries. Across a suite of challenging benchmarks, GLU consistently improves reconstruction fidelity over reduced-order, convolutional, neural operator, and attention-based baselines, better preserving multi-scale structures. For forecasting, a hierarchical Leader-Follower Dynamics module evolves the latent state with substantially reduced memory growth, maintains stable rollout behavior and delays error accumulation in nonlinear dynamics. On a realistic turbulent combustion dataset, it further preserves not only sharp fronts and broadband structures in multiple physical fields, but also their cross-channel thermo-chemical couplings. Scalability tests show that these gains are achieved with substantially lower memory growth than comparable attention-based baselines. Together, these results establish GLU as a flexible and computationally practical paradigm for sparse digital twins.

Digital twins of complex physical systems are expected to infer unobserved states from sparse measurements and predict their evolution in time, yet these two functions are typically treated as separate tasks. Here we present GLU, a Global-Local-Uncertainty framework that formulates sparse reconstruction and dynamic forecasting as a unified state-representation problem and introduces a structured latent assembly to both tasks. The central idea is to build a structured latent state that combines a global summary of system-level organization, local tokens anchored to available measurements, and an uncertainty-driven importance field that weights observations according to the physical informativeness. For reconstruction, GLU uses importance-aware adaptive neighborhood selection to retrieve locally relevant information while preserving global consistency and allowing flexible query resolution on arbitrary geometries. Across a suite of challenging benchmarks, GLU consistently improves reconstruction fidelity over reduced-order, convolutional, neural operator, and attention-based baselines, better preserving multi-scale structures. For forecasting, a hierarchical Leader-Follower Dynamics module evolves the latent state with substantially reduced memory growth, maintains stable rollout behavior and delays error accumulation in nonlinear dynamics. On a realistic turbulent combustion dataset, it further preserves not only sharp fronts and broadband structures in multiple physical fields, but also their cross-channel thermo-chemical couplings. Scalability tests show that these gains are achieved with substantially lower memory growth than comparable attention-based baselines. Together, these results establish GLU as a flexible and computationally practical paradigm for sparse digital twins.

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.

Machine learning (ML) surrogate models offer a promising route to accelerate material property prediction, bypassing costly atomistic simulations. Here, we introduce IsothermODE, a neural ordinary differential equation (NODE) framework for reconstructing full uptake and heat of adsorption $$\left(\Delta {H}_{{\rm{ads}}}\right)$$ isotherms for CO2 adsorption in metal-organic frameworks (MOFs) using only sparse pressure data. Unlike traditional ML models, IsothermODE leverages the intrinsic structure of differential equations to produce smooth, physically-consistent predictions that generalize across wide pressure ranges. We demonstrate high-fidelity interpolation and extrapolation, even with only five pressure points. To address the stochasticity inherent in Grand Canonical Monte Carlo (GCMC) simulations, we integrate uncertainty quantification, yielding tight bounds on predicted enthalpy curves. We further interpret the learned latent dynamics in terms of adsorption thermodynamics and textural properties, offering insight into structure-property relationships. Finally, we demonstrate IsothermODE’s long-range interpolation and extrapolation capabilities with sparse isotherm data (5 pressure points) and large incomplete intervals featuring missing data between 4–40 (case 1) and 25–50 (case 2) bars. IsothermODE provides a fast, robust alternative to simulation-heavy workflows, enabling scalable screening and design of next-generation carbon capture materials.

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 or mixture-based rate behavior, which is critical in many combustion and chemical systems and typically requires empirical falloff formulations such as Troe or SRI, or data-based interpolation or polynomial fits such as PLOG or Chebyshev Polynomials. Here, we develop Kolmogorov-Arnold Chemical Reaction Neural Networks (KA-CRNNs) that generalize CRNNs by modeling each kinetic parameter as a learnable function of third-body concentrations using Kolmogorov-Arnold activations. This structure maintains the Arrhenius and mass action interpretability and physical constraints of a vanilla CRNN while enabling assumption-free inference of global and collider-specific pressure effects directly from data. Two proof-of-concept reaction studies are presented to highlight the capability of KA-CRNNs to accurately reproduce pressure-dependent and collider-specific kinetics across a range of temperatures, pressures, and bath gas mixtures, extracting meaningful and generalizable models from sparse training data and significantly outperforming interpolative approaches (2.88x reduction in MSE). The framework establishes a foundation for data-driven discovery of extended kinetic behaviors in complex reacting systems, advancing interpretable and physics-constrained approaches for chemical model inference.

The rapid growth in the use of lithium-ion batteries (LIBs) in electric vehicles, consumer electronics, and renewable energy storage has made effective end-of-life management essential. Recycling LIBs is critical not only for resource recovery and environmental protection but also for ensuring safety and economic viability. This review focuses on the preprocessing technologies that precede typical recovery processes, including disassembly, sorting, discharging, electrolyte removal, dismantling, thermal treatment, separation, and flotation. These steps play a foundational role in determining the efficiency, safety, and environmental impact of LIB recycling. LIBs pose substantial fire and explosion risks due to residual charge, flammable electrolytes, and reactive materials. The conditions and successive progression of the exothermic reactions which lead to thermal runaway has been discussed. It also explores secure deactivation techniques such as external circuit discharge, saline immersion, and thermomechanical methods, alongside fire prevention strategies including the use of flame retardants, elimination of oxidants, and reduction of heat generation and accumulation. Challenges and future directions are outlined, highlighting the need for standardized designs, automation, and safer, more sustainable recycling infrastructure. This review is distinguished by its focused analysis of preprocessing and deactivation steps, with particular attention to the thermal safety engineering aspects of LIB recycling.

Pretraining on large-scale collections of PDE-governed spatiotemporal trajectories has recently shown promise for building generalizable models of dynamical systems. Yet most existing PDE foundation models rely on deterministic Transformer architectures, which lack generative flexibility for many science and engineering applications. We propose Flow Marching, an algorithm that bridges neural operator learning with flow matching motivated by an analysis of error accumulation in physical dynamical systems, and we build a generative PDE foundation model on top of it. By jointly sampling the noise level and the physical time step between adjacent states, the model learns a unified velocity field that transports a noisy current state toward its clean successor, reducing long-term rollout drift while enabling uncertainty-aware ensemble generations. Alongside this core algorithm, we introduce a Physics-Pretrained Variational Autoencoder (P2VAE) to embed physical states into a compact latent space, and an efficient Flow Marching Transformer (FMT) that combines a diffusion-forcing scheme with latent temporal pyramids, achieving up to 15x greater computational efficiency than full-length video diffusion models and thereby enabling large-scale pretraining at substantially reduced cost. We curate a corpus of ~2.5M trajectories across 12 distinct PDE families and train suites of P2VAEs and FMTs at multiple scales. On downstream evaluation, we benchmark on unseen Kolmogorov turbulence with few-shot adaptation, demonstrate long-term rollout stability over deterministic counterparts, and present uncertainty-stratified ensemble results, highlighting the importance of generative PDE foundation models for real-world applications.

Combustion in nanocomposites involves intricate coupling between chemical reactions and transport phenomena across multiple scales and phases, complicating the development of unified theories. In this study, we present a theoretical and experimental framework that can serve as the foundation for a unified theory of combustion wave dynamics and instabilities in nanocomposites. Using high-speed microscopic imaging, the flame morphology and combustion wave behavior are characterized across a range of reactivity levels. We find that wave speed correlates more strongly with reactivity than predicted by classical laminar flame theory but also decreases due to combustion instability when reactivity exceeds a certain level. We reveal that this strong correlation is attributed to heterogeneous flame structures altered by nanoparticle sintering. Unstable combustion waves feature highly corrugated flame fronts that are prone to quenching from significant heat loss in sintered nanoparticles. We further validate wave stability analysis for unseen particle morphology using macroscopic observations. These insights lay the groundwork for theory-guided strategies to control combustion wave behavior and enable the design of reactive nanocomposites that move beyond empirical trial-and-error methods.

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.

The large design space of metal-organic frameworks (MOFs) has prompted the utilization of deep learning to drive material design. Nonetheless, the prediction of key thermodynamic properties, such as heat of adsorption ( $$\Delta {H}_{{\rm{ads}}}$$ ), remains largely unexplored for CO2 adsorption in MOFs. Herein, we present IsothermNet, a high-throughput graph neural network designed to estimate uptake and $$\Delta {H}_{{\rm{ads}}}$$ over 0–50 bars, enabling high-quality full isotherm reconstruction (PCC: 0.73–0.95 [uptake], 0.76–0.88 [ $$\Delta {H}_{{\rm{ads}}}$$ ]). We further bridged these adsorption properties to uptake behaviors (i.e., isotherm shapes/types) and structural information by performing detailed ablation studies to investigate the relative importance of local and global features in relation to predictive performance. This comparative analysis facilitated the discovery of a (1) physically-interpretable and (2) analytically-derived universal descriptor set capable of illustrating interdependencies between easily-computed, accessible textural information and extrinsic adsorption properties. When used cooperatively with IsothermNet, these descriptors enable efficient material screening, accelerating high-performance MOF discovery for CO2 capture.

Single-crystal (SC) Ni-rich cathode materials have attracted great attention for Li-ion battery applications due to their outstanding cyclability. However, the high temperature required for synthesizing SC also causes damage to temperature-sensitive Ni-rich cathode materials. Severe surface damage can result, even without notable bulk property degradation. Fortunately, we reveal that the surface damage can be mitigated by applying molten salt as an in situ protection agent to the particle surface during the high-temperature calcination. Detailed morphology evolution and near-surface features captured by in situ and ex situ techniques demonstrate that even a small amount of molten salt can effectively enclose particles during calcination. As a result, a solid–liquid–gas interface is built to replace the solid–gas interface, inhibiting the irreversible loss of lithium and oxygen to the high-temperature environment. Overall, SC particles synthesized with a suitable amount of molten salt addition show fewer surface defects and impurities than those without molten salt, leading to an enhanced electrochemical performance. This study highlights the importance of controlling surface damage in the production of high-performance SC Ni-rich cathode materials.

, from nucleation to elongation and ultimately termination. We also examine the dynamic behaviors of catalyst nanoparticles and chirality-controlled growth processes, emphasizing how these insights contribute to advancing the field. Finally, in the concluding section, we propose future directions for advancements of computational approaches toward deeper understanding of CNT growth mechanisms and better support of CNT manufacturing.

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 2× 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.

Despite the potential of nanoenergetics as promising energy sources with high energy densities and fast energy release, our limited ability to predict combustion speeds restricts the utilization of nanoenergetics. Here, we provide a comprehensive analysis of thermal microstructures subject to heterogeneous reactions and propose a new scaling for combustion wave speeds. To control reaction heterogeneity, two different particle interfacial morphologies of physically mixed and core-shell Al/CuO nanoparticles were synthesized. The combustion dynamics and temperature fields were obtained at micrometer-scale resolutions using high-speed and infrared cameras. Experiments showed that the core-shell Al/CuO exhibiting less reaction heterogeneity had a faster wave speed than the physically mixed counterpart, although the measured chemical reaction rates were lower. By employing the thermal structure analysis, we found that the shortened preheat zone and the lengthened reaction zone, attributed to the lower reaction onset temperature and reaction rate, led to the increased wave speed despite the lower reaction rate in the core-shell Al/CuO. From these analyses, we developed a new scaling that describes the combustion wave speeds in nanoenergetics based on intrinsic properties and thermal structures for both morphologies.

Although thermal waves are ubiquitous in nature and engineering, the development of diagnostic tools capable of elucidating the roles of reaction and transport remains an unmet need. This limits our comprehension of the physics and ability to predict wave dynamics. Here we demonstrate that thermal properties and chemical kinetics can be learned directly from observing thermal wave dynamics, using partial differential equation-constrained optimization. This enables the determination of unobserved reaction rates without the need for a comprehensive measurement of all state variables, given the model space constrained by governing equations. Examples include steady planar waves and unsteady pulsating waves of which dynamics are commonly observed in nature. We show successful learning of thermal properties and chemical kinetics and reconstruction of wave dynamics with the inferred properties, which enables the comprehension of the intricate reaction-transport coupling from thermal data. Thermal waves describe the propagation of heat in chemically reacting flows such as combustion processes. Here the authors establish a differential-equation based framework that reveals reaction and material properties directly from analyzing thermal waves.

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 Schr\"odinger 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.

In the realm of combustion and reacting flow modeling, the calibration of the kinetic model parameters often relies on experimental data. However, not all data obtained under different experimental conditions (pressure, temperature, equivalence ratio, etc.) hold equal weight or feasibility for effective model calibration. Consequently, experimental design emerges as an important topic in combustion kinetics, aiming at identifying the most informative conditions computationally. In this work, we built a Bayesian experimental design framework enabling the highly efficient uncertainty reduction of kinetic parameters and model predictions. Our contributions are 3-fold. First, inspired by previous works aiming at uncertainty reduction of prediction or selected parameters, we proposed two new optimization objectives via model linearization oriented directly to quantities of interest (QoI), parameter-oriented and prediction-oriented design, for uncertainty reduction of specific parameters and prediction targets, respectively. We conducted theoretical analyses to link Bayesian information gain with dimensionless sensitivity (referred to as impact numbers) and to demonstrate the necessity of implementing QoI-oriented Bayesian experimental design (QBED). Second, neural network response surfaces with both kinetic parameters and experimental conditions as inputs were applied to the experimental design so that a single unified response surface can provide fast, differentiable predictions under a wide range of conditions. It not only facilitates gradient-based design but also accelerates enumeration-based design by parallel computing. Third, we integrated the posterior approximation by linearizing response surfaces with gradient ascent for design optimization. Comparisons with the enumeration-based method demonstrate that gradient-based design usually has a higher average information gain, while enumeration-based design, when assisted by the unified response surface, shows a faster computational speed with acceptable suboptimality. Comprehensive numerical experiments were conducted on the ignition delay times and laminar flame speeds of methanol. Statistical analysis was performed to prove the effectiveness of our methods. The dynamic evolution of uncertainty reduction was unraveled and is well supported by the insights from impact numbers. The proposed method can finish one design-inference iteration in 0.5 s in the 3-D design space and 1.6 s in the 9-D space on an NVIDIA GeForce RTX 2080 Ti graphics processing unit. The QBED source code was made available online.

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.

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.