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At least 1,369 records · Page 76

Observational Constraints on Warm Cloud Microphysical Processes Using Machine Learning and Optimization Techniques

We introduce new parameterizations for autoconversion and accretion rates that greatly improve representation of the growth processes of warm rain. The new parameterizations capitalize on machine‐learning and optimization techniques and are constrained by in situ cloud probe measurements from the recent Atmospheric Radiation Measurement Program field campaign at Azores. The uncertainty in the new estimates of autoconversion and accretion rates is about 15% and 5%, respectively, outperforming existing parameterizations. Our results confirm that cloud and drizzle water content are the most important factors for determining accretion rates. However, for autoconversion, in addition to cloud water content and droplet number concentration, we discovered a key role of drizzle number concentration that is missing in current parameterizations. The robust relation between autoconversion rate and drizzle number concentration is surprising but real, and furthermore supported by theory. Thus, drizzle number concentration should be considered in parameterizations for improved representation of the autoconversion process.

54 ENVIRONMENTAL SCIENCES↗

Sandtank-ML: An Educational Tool at the Interface of Hydrology and Machine Learning

Hydrologists and water managers increasingly face challenges associated with extreme climatic events. At the same time, historic datasets for modeling contemporary and future hydrologic conditions are increasingly inadequate. Machine learning is one promising technological tool for navigating the challenges of understanding and managing contemporary hydrological systems. However, in addition to the technical challenges associated with effectively leveraging ML for understanding subsurface hydrological processes, practitioner skepticism and hesitancy surrounding ML presents a significant barrier to adoption of ML technologies among practitioners. In this paper, we discuss an educational application we have developed—Sandtank-ML—to be used as a training and educational tool aimed at building user confidence and supporting adoption of ML technologies among water managers. We argue that supporting the adoption of ML methods and technologies for subsurface hydrological investigations and management requires not only the development of robust technologic tools and approaches, but educational strategies and tools capable of building confidence among diverse users.

54 ENVIRONMENTAL SCIENCES↗

Postmortem and Antemortem Forensic Assessment of Pediatric Fracture Healing from Radiographs and Machine Learning Classification

A timeline of pediatric bone healing using fracture healing characteristics that can be assessed solely using radiographs would be practical for forensic casework, where the fracture event may precede death by days, months, or years. However, the dating of fractures from radiographs is difficult, imprecise, and lacks consensus, as only a few aspects of the healing process are visible on radiographs. Multiple studies in both the clinical and forensic literature have attempted to develop a usable scale to assess pediatric bone healing on radiographs using various healing characteristics. In contrast to the orthopedic definition, a fracture in forensic casework is only considered to be healed when the area around the fracture has been remodeled to the point that the fracture is difficult to detect on a radiograph or on the surface of the bone itself, a process that can take several years. We subjectively assessed visible characteristics of healing in radiograms of fractures occurring in 942 living children and adolescents. By dividing these assessments into learning and test (validation) sets, the accuracy of a newly proposed fracture healing scale was compared to a previous study. Two machine learning models were used to test predictions of the new scale. All three models produced similar estimates with substantial imprecision. Results corroborate the Malone model with an independent dataset and support the efficacy of using less complex models to estimate fracture age in children.

60 APPLIED LIFE SCIENCES↗

Recent Progress on Surface Water Quality Models Utilizing Machine Learning Techniques

Surface waterbodies are heavily exposed to pollutants caused by natural disasters and human activities. Empowering sensor technologies in water quality monitoring, sufficient measurements have become available to develop machine learning (ML) models. Numerous ML models have quickly been adopted to predict water quality indicators in various surface waterbodies. This paper reviews 78 recent articles from 2022 to October 2024, categorizing water quality models utilizing ML into three groups: Point-to-Point (P2P), which estimates the current target value based on other measurements at the same time point; Sequence-to-Point (S2P), which utilizes previous time series data to predict the target value at one time point ahead; and Sequence-to-Sequence (S2S), which uses previous time series data to forecast sequential target values in the future. The ML models used in each group are classified and compared according to water quality indicators, data availability, and model performance. Widely used strategies for improving performance, including feature engineering, hyperparameter tuning, and transfer learning, are recognized and described to enhance model effectiveness. The interpretability limitations of ML applications are discussed. This review provides a perspective on emerging ML for surface water quality models.

machine learning (ML)↗

Transcriptomics-based Machine Learning Analysis Predicts Space-Exposed Murine Livers

Limited sample sizes, high data dimensionality, and sensitivity to technical and biological variability of next generation sequencing (NGS), has typically limited machine learning (ML) in space studies and further study of radiation effects. However, pooling smaller studies while addressing intra- and inter-study variabilities allows for ML predictive modeling. Here, integration methods were applied to whole transcriptome shotgun sequencing (RNAseq) data from 6 mouse liver GeneLab datasets (GLDS) with a total of 113 spaceflight and ground-control samples to determine top features relevant to spaceflight including the effect of radiation exposure. Data was normalized within each study, then merged and scaled across all datasets. Data dimensionality was reduced using a minimum redundancy maximum relevance (MRMR) methodology. The top MRMR features were used to predict spaceflight vs. ground-control samples using a Random Forest (RF) classifier with 5-fold cross validation (CV). The ML-based gene sets were further compared against differential gene expression results from individual GLDS. CV training using the top 100 MRMR genes show averages of 86% accuracy and 0.95 AUC value on the validation set over 5 folds (Figure 1A). Baseline set analysis on differentially expressed genes (DEGs) identified using padj ≤ 0.05 show 811 or 68 DEGs overlapping between at least 2 or 3 studies, respectively (Figure 1B). Over-representation analysis showed overlapping biological processes related to fatty acid and lipid metabolism. Set analysis between the MRMR features and the DEGs showed 60 or 8 genes overlapping with at least 1 or 2 studies, respectively. MRMR feature selection and ensemble ML methods (e.g. RF) improve performance relative to a Naïve Bayes classifier when NGS data sets are analyzed. A challenge of applying ML methods across heterogeneous NGS data is accounting for signal:noise ratio. Here, signal validation across studies was shown by intersecting sets between top MRMR genes and DEGs from RNASeq analysis. Non-intersecting sets introduce opportunity to explore spaceflight relevant genes and implementing ML methods across existing NGS datasets may overcome sample size limitations. ML coupled with existing analytical methods enhances understanding of disease by revealing common underlying pathways across datasets.

Machine Learning↗

Machine learning materials properties with accurate predictions, uncertainty estimates, domain guidance, and persistent online accessibility

One compelling vision of the future of materials discovery and design involves the use of machine learning (ML) models to predict materials properties and then rapidly find materials tailored for specific applications. However, realizing this vision requires both providing detailed uncertainty quantification (model prediction errors and domain of applicability) and making models readily usable. At present, it is common practice in the community to assess ML model performance only in terms of prediction accuracy (e.g. mean absolute error), while neglecting detailed uncertainty quantification and robust model accessibility and usability. Here, we demonstrate a practical method for realizing both uncertainty and accessibility features with a large set of models. We develop random forest ML models for 33 materials properties spanning an array of data sources (computational and experimental) and property types (electrical, mechanical, thermodynamic, etc). All models have calibrated ensemble error bars to quantify prediction uncertainty and domain of applicability guidance enabled by kernel-density-estimate-based feature distance measures. All data and models are publicly hosted on the Garden-AI infrastructure, which provides an easy-to-use, persistent interface for model dissemination that permits models to be invoked with only a few lines of Python code. We demonstrate the power of this approach by using our models to conduct a fully ML-based materials discovery exercise to search for new stable, highly active perovskite oxide catalyst materials.

domain of applicability↗

Multi-Source Machine Learning and Thermoplastics Enhanced Aerostructure Manufacturing (mTEAM)

RTX Technology Research Center (RTRC), together with Collins Aerospace (Collins) and Oak Ridge National Laboratory (ORNL) has developed an Artificial Intelligence (AI) / Machine Learning (ML) guided solution to advance the manufacturing and assembly of high performance and lightweight thermoplastic composite (TPC) aerospace products. The solution aims to lower risk, cost and lead time for induction heating based welding and consolidation processes for TPC structure. The cost and lead time of part and material specific process development for induction welding (IW) and induction consolidation will be reduced by replacing traditional empirical methods with optimization methods that merge AI/ML and physics-based process simulations and process experiments with sensing and controls. TPC-IW process development is empirical in nature, and uncertainties in material & process behavior exist near & far from the induction coil. Physics-based simulations can be leveraged directly for process optimization but can be too computationally expensive to run in high fidelity and real time to do robust process optimization. The key impact of successful TPC induction consolidation and welding is cost & lead time reduction for part & material specific consolidation and welding recipes. This is an enabler for more rapid deployment of TPC structures via joining assembly, which can reduce energy & cost intensive usage of autoclaves & ovens. The solution aimed to advance the U.S. Department of Energy’s interests in using thermoplastics and automation in composite manufacturing for improvement of products for existing markets via increased production speeds, reduced costs, and lowered use of energy. Welded TPC structures can offer significant weight & energy savings for high-value commercial aerospace & industrial applications compared to metal & thermoset composite structures assembled by mechanical fastening and/or adhesive bonding. The project was organized into two Budget Periods. Budget Period 1 (BP1) was 15 months and its goal was to perform ML process optimization framework development & deployment on lab-coupon aerostructure components. A Go/No-Go Review was performed at the end of BP1 to verify fulfilment of key tasks & milestones to justify a Go Decision to move into the next Budget Period. Budget Period 2 (BP2) was 12 months and its goal was the deployment of the ML framework for ML process optimization of pilot industrial scale aerostructure components. The overall project aim was to develop & demonstrate ML-enhanced modeling framework that learns process-property mapping from multiple data sources at different fidelities. During BP1, the team accomplished key tasks & milestones to demonstrate the concept of multi-source ML for TPC aerostructure consolidation and assembly. First, the team completed documentation of induction based TPC heating requirements including baseline metrics to compare measured results against. Next the team completed demonstration of data generation from physics-based simulations for ML surrogate model generation and demonstrated the integration of physics-based simulation data into multi-source AI/ML algorithms. In parallel, the team established the lab-coupon scale induction welding system and completed a process to label and reduce generated data from physics-based simulation and experiments for ML surrogate models to enable multi-source ML model training & testing. To complete BP1, the team integrated physics-based simulation data and experimental data into multi-source ML algorithms. This was based on the team completing ML deployment of the induction welding on a lab system at RTRC and AI/ML deployment on existing induction welding line at Collins. ORNL visited both Collins and RTRC sites to witness the TPC induction welding process. Then, ORNL designed and constructed a new version of their vision-based sensing system better adapted to acquire process signals of the TPC induction welding process for process anomaly and defect detection. In BP2, the team accomplished key tasks & milestones to scale up multi-source ML for TPC aerostructure consolidation and assembly from the lab-coupon scale to the pilot-industrial scale. In BP2, the team demonstrated real time anomaly & defect detection via experiments performed by ORNL & RTRC. The team completed ML-optimization heating trials for TPC induction consolidation at Collins, and the team confirmed pilot industrial scale experimental data from Collins was compatible with the developed ML pipeline from RTRC. The team completed sub-element scale ML process optimization demonstration at RTRC, where the team leveraged RTRC’s robotic TPC welding setup to de-risk the ML process optimization by performing ML analysis of recorded temperatures to account for complex part features. Then, the team applied its ML-derived control strategies and ML process optimization framework at Collins to the pilot-industrial scale on a demo skin-stiffener part representative of a nacelle aerostructure fan cowl section. The key innovation is the AI/ML framework enabling effective process development of high performance, lightweight, energy efficient TPCs for composite aircraft structures.

36 MATERIALS SCIENCE↗

Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: Application to ternary random alloys

We present a scale-bridging approach based on a multi-fidelity (MF) machine-learning (ML) framework leveraging Gaussian processes (GP) to fuse atomistic computational model predictions across multiple levels of fidelity. Through the posterior variance of the MFGP, our framework naturally enables uncertainty quantification, providing estimates of confidence in the predictions. We used density functional theory as high-fidelity prediction, while a ML interatomic potential is used as low-fidelity prediction. Practical materials’ design efficiency is demonstrated by reproducing the ternary composition dependence of a quantity of interest (bulk modulus) across the full aluminum–niobium–titanium ternary random alloy composition space. The MFGP is then coupled to a Bayesian optimization procedure, and the computational efficiency of this approach is demonstrated by performing an on-the-fly search for the global optimum of bulk modulus in the ternary composition space. The framework presented in this manuscript is the first application of MFGP to atomistic materials simulations fusing predictions between density functional theory and classical interatomic potential calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A New Perspective of Post-Weld Baking Effect on Al-Steel Resistance Spot Weld Properties through Machine Learning and Finite Element Modeling

The root cause of post-weld baking on the mechanical performance of Al-steel dissimilar resistance spot welds (RSWs) has been determined by machine learning (ML) and finite element modeling (FEM) in this study. A deep neural network (DNN) model was constructed to associate the spot weld performance with the joint attributes, stacking materials, and other conditions, using a comprehensive experimental dataset. The DNN model positively identified that the post-weld baking reduces the joint performance, and the extent of degradation depends on the thickness of stacking materials. A three-dimensional finite element (FE) model was then used to investigate the root cause and the mechanism of the baking effect. It revealed that the formation of high thermal stresses during baking, from the mismatch of thermal expansion between steel and Al alloy, causes damage and cracking of the brittle intermetallic compound (IMC) formed at the interface of the weld nugget during welding. This in turn reduces the joint performance by promoting undesirable interfacial fracture when the welds were subjected to externally applied loads. The FEM model further revealed that increase in structural stiffness, because of increase in steel sheet thickness, reduces the thermal stresses at the interface caused by the thermal expansion mismatch and consequently lessens the detrimental effect of post-weld baking on the joint performance.

36 MATERIALS SCIENCE↗

Empirical probability and machine learning analysis of m , n = 2, 1 tearing mode onset parameter dependence in DIII-D H-mode scenarios

m, n = 2, 1 tearing mode onset empirical probability and machine learning analyses of a multiscenario DIII-D database of over 14 000 H-mode discharges show that the normalized plasma beta, the rotation profile, and the magnetic equilibrium shape have the strongest impact on the 2,1 tearing mode stability, in qualitative agreement with neoclassical tearing modes (m and n are the poloidal and toroidal mode numbers, respectively). In addition, 2,1 tearing modes are most likely to destabilize when n > 1 tearing modes are already present in the core plasma. The covariance matrix of tearing sensitive plasma parameters takes a nearly block-diagonal form, with the blocks incorporating thermodynamic, current and safety factor profile, separatrix shape, and plasma flow parameters, respectively. This suggests a number of paths to improved stability at fixed pressure and edge safety factor primarily by preserving a minimum of 1 kHz differential rotation, increasing the minimum safety factor above unity, using upper single null magnetic configuration, and reducing the core impurity radiation. In addition, lower triangularity, lower elongation, and lower pedestal pressure may also help to improve stability. Furthermore, the electron and ion temperature, collisionality, resistivity, internal inductance, and the parallel current gradient appear to only weakly correlate with the 2,1 tearing mode onsets in this database.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Accuracy of predictions made by machine learned models for biocrude yields obtained from hydrothermal liquefaction of organic wastes

Hydrothermal liquefaction (HTL) has potential for converting abundant wet organic wastes into renewable fuels. Because HTL consists of a complex reaction network, deterministic, physics-based prediction of its biocrude yield is prohibitively difficult. Data-driven methods provide an alternative to the physics-based approach; however, rigorous testing must be performed to ensure the accuracy of predictions made by data-driven methods. To this end, a data set was assembled consisting of 570 data points appearing in the open literature. The data set was divided into training, validation, and test sub-sets and used for evaluating different machine learning regression approaches to predict biocrude yield. Among the tested algorithms, Random Forest and eXtreme Gradient Boosting (XGBoost) predicted biocrude yields in a test set that had not been used for training with the greatest accuracy, with root mean square errors (RMSE) of 8.34 and 8.57, respectively. Further refinement of the Random Forest model reduced its RMSE to 8.07. In comparison, predictions of a series of literature models resulted in RMSE ranging from 9.16 in the most accurate case to 27.6 in the least accurate; most literature models yielded RMSE values > 10. Using biocrude yield predictions from the most accurate Random Forest model and a probabilistic economic analysis found that the model accuracy is sufficient to prioritize allocation of resources based on projected minimum fuel selling price. In our report the models and analysis represent a major advance in the ability to use readily available data to predict biocrude yields on new feedstocks that have not previously been studied.

42 ENGINEERING↗

Machine learning prediction of the mechanical properties of refractory multicomponent alloys based on a dataset of phase and first principles simulation

In this work, a dataset including structural and mechanical properties of refractory multicomponent alloys was developed by fusing computations of phase diagram (CALPHAD) and density functional theory (DFT). The refractory multicomponent alloys, also named refractory complex concentrated alloys (CCAs) which contain 2–5 types of refractory elements were constructed based on Special Quasi-random Structure (SQS). The phase of alloys was predicted using CALPHAD and the mechanical property of alloys with stable and single body-centered cubic (BCC) at high temperature (over 1,500°C) was investigated using DFT-based simulation. As a result, a dataset with 393 refractory alloys and 12 features, including volume, melting temperature, density, energy, elastic constants, mechanical moduli, and hardness, were produced. To test the capability of the dataset on supporting machine learning (ML) study to investigate the property of CCAs, CALPHAD, and DFT calculations were compared with principal components analysis (PCA) technique and rule of mixture (ROM), respectively. It is demonstrated that the CALPHAD and DFT results are more in line with experimental observations for the alloy phase, structural and mechanical properties. Furthermore, the data were utilized to train a verity of ML models to predict the performance of certain CCAs with advanced mechanical properties, highlighting the usefulness of the dataset for ML technique on CCA property prediction.

36 MATERIALS SCIENCE↗

Use of Machine Learning on PMU Data for Transmission System Fault Analysis

Synchrophasor technology has been used for monitoring, control, and protection of bulk power system for over 10 years. Deployment of phasor measurement units (PMUs) in the USA power system has surpassed 3000 units installed in the transmission substations as stand-alone intelligent electronic devices (IEDs) or as a software add-on to other devices such as digital protective relays (DPRs) or digital fault recorders (DFRs). By now, thousands of terabytes of PMU data may have been captured and stored by various transmission system operators (TSOs) and independent system operators (ISOs). This creates an opportunity to deploy advanced machine learning (ML) techniques to detect and classify faults recorded by PMUs automatically to be used by the system operators for rapid, critical decision-making when manual analysis of the past or unfolding events is not feasible. In this paper we offer a brief background on how the automated fault analysis may be done using DPR and/or DFR data, and compare some of the legacy approaches to the new ML approaches in the context of the system-wide PMU recordings. We then offer insights from developing practical ML solutions that have been applied on field recordings captured by close to 450 PMUs from all three US interconnections (Western, Eastern and ERCOT) over two years (2016-2017). We identify and illustrate ML challenges we addressed: inaccurate data, data with scarce and temporally imprecise fault labels, data recorded by PMUs sparsely located at substations resulting in the fault records taken afar from the ends of the faulted lines, data containing only positive sequence values, and data taken at different voltage levels. We then illustrate the ML model results for fault analysis under different application scenarios. The novelty of this study is not only in the design, implementation, and performance analysis of the ML algorithms, but also in the use of advanced fault modelling and simulation approaches to improve the training results when developing supervised ML models for fault detection and classification. Extensive simulations of faults were conducted on a 14-bus power system to create a training dataset with over 1400 accurately labelled faults. This dataset was applied to enhance the accuracy of fault detection and classification of machine learning-based models trained with small number of labelled faults in large datasets recorded in the grid interconnections ranging from 5,000 to 70,000 buses.

Synchrophasors, Machine Learning, Fault Analysis, ↗

Machine Learning in Nuclear Thermal Hydraulics, Part 2: Opportunities and Perspectives

This paper summarizes the issues in nuclear thermal hydraulics (NTH), mainly from the three named aspects, and illustrates potential opportunities of machine learning (ML) applications in dealing with these issues. These issues are problems in simultaneously realizing computational efficiency and accuracy of system thermal hydraulic (STH) modeling and simulation, uncertainty in the scaling analysis for the best-estimate calculations of transient and accident analysis, and difficulties in optimal data production and usage for the development and assessment of evaluation models. Due to ML uncertainty, data insufficiency, and lack of cognition about how to efficiently incorporate knowledge and data, challenges of adapting ML techniques still exist. Accordingly, several perspectives are proposed to provide insights for ML applications in solving these issues.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Machine Learning Accelerates Innovation in Perovskite Manufacturing Scale-up (Final Technical Report (FTR))

We propose to address the challenge of the vast parameter space associated with perovskite manufacturing optimization, by developing a machine learning (ML)-assisted optimization framework for a scalable perovskite PV manufacturing tool. This framework will be interpretable, sequential, and rapidly adaptable to upgraded systems (e.g., via transfer learning). The tool is an open-air rapid spray plasma process (RSPP) of perovskite films, which has already been established at Stanford and is a unique platform to test and deploy the proposed ML-guided framework because the RSPP technique is able to conduct optimization experiments with a high throughput, and easily adjust a wide range of process variables.

14 SOLAR ENERGY↗

Machine learning guided discovery of superconducting calcium borocarbides

Pursuit of superconductivity in light-element systems at ambient pressure is of great experimental and theoretical interest. In this work, we combine a machine learning (ML) method with first-principles calculations to efficiently search for the energetically favorable ternary Ca-B-C compounds. Three layered borocarbides (stable CaBC 5 and metastable Ca 2 BC 11 and CaB 3 C 3 ) are predicted to be phonon-mediated superconductors at ambient pressure. The stable CaBC 5 and the low-energy metastable Ca 2 BC 11 (with formation energy only 9.5 meV/atom above the convex hull) have a superconducting T c of 5.2 and 8.9 K, respectively. While the hexagonal CaB 3 C 3 possesses a T c of 26.1 K, it is metastable with formation energy of 153 meV/atom above the convex hull. The ML-guided approach opens up a way for greatly accelerating the discovery of new high-T c superconductors.

36 MATERIALS SCIENCE↗

Reconstructing PM 2.5 Data Record for the Kathmandu Valley Using a Machine Learning Model

This paper presents a method for reconstructing the historical hourly concentrations of particulate matter 2.5 (PM2.5) over the Kathmandu Valley from 1980 to the present. The method uses a machine learning model that is trained using PM2.5 readings from US Embassy (Phora Durbar) as a ground truth, and the meteorological data from Modern-Era Retrospective Analysis for Research and Applications v2 (MERRA2) as input. The Extreme Gradient Boosting (XGBoost) model acquires a credible 10-fold cross-validation (CV) score of ~83.4%, an r2-score of ~84%, a Root Mean Square Error (RMSE) of ~15.82 µg/m3, and a Mean Absolute Error (MAE) of ~10.27 µg/m3. Further demonstrating the model's applicability to years other than those for which truth values are unavailable, the multiple cross-test with an unseen data set offered r2-scores for 2018, 2019, and 2020 ranging from 56% to 67%. The model-predicted data agrees with true values and indicates that MERRA2 underestimates PM2.5 over the region. It strongly agrees with ground-based evidence showing substantially higher mass concentrations in the dry pre- and post-monsoon seasons than in the monsoon months. It also shows a strong anti-correlation between PM2.5 concentration and humidity. The results also demonstrate that none of the years fulfilled the annual mean air quality index (AQI) standards set by the World Health Organization (WHO).

machine learning↗

Free-Energy Landscapes and Surface Dynamics in Methane Activation on Ni(511) via Machine Learning and Enhanced Sampling

Methane activation on stepped Ni(511) surfaces involves the rearrangement of surface atoms as the chemical reaction proceeds. This process is particularly sensitive to temperature. Using machine-learned interatomic potentials (MLIPs) coupled with enhanced sampling techniques, we investigate the activation of methane under realistic operando conditions. Our analysis reveals that methane dissociation occurs predominantly at step-edge nickel atoms. As CH x (where x = 3 or 4) species bind to additional surface nickel atoms, their reduced mobility leads to entropic penalties that suppress certain configurations and transition states. This is reflected in the underlying free energy surfaces, where configurations such as methyl binding to hollow sites and activation routes involving two nickel atoms become unfavorable as temperature increases. At elevated temperatures, methane activation extends from step-edge sites to terrace regions because of reduced free-energy barriers and enhanced surface dynamics. By decomposing the free-energy into enthalpic and entropic contributions, we uncover temperature-dependent shifts in the preferences of methane for the relevant active sites and arrive at a detailed molecular picture of methane activation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗