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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3

Analysis of a Heat Balance Experiment in the TREAT Reactor with SPARTA and OpenMC

This article presents the interpretation of a heat balance experiment in TREAT using the SPARTA methodology and an OpenMC model. The study examines the effects of control rods and temperature variations on the effective multiplication factor ($k_{\rm eff}$) and correction factors. Results indicate that both core temperature and rod positions have a linear effect on $k_{\rm eff}$ and correction factors in the upper-west channel. A critical hypothesis of SPARTA was validated: reactivities and correction factors can be obtained by linearly combining individual effects. The previously considered negligible effect of temperature on correction factors was found to be significant, necessitating updates to the SPARTA methodology. By fitting an exponential curve to mean temperature data, SPARTA's accuracy and convergence have been improved. Comparisons between SPARTA and OpenMC showed consistent reactivity removal due to temperature increase. While SPARTA effectively interprets complex transients, simpler methods may suffice when correction factors have minimal influence on reactivity calculations.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Resource selection functions based on hierarchical generalized additive models provide new insights into individual animal variation and species distributions

Habitat selection studies are designed to generate predictions of species distributions or inference regarding general habitat associations and individual variation in habitat use. Such studies frequently involve either individually indexed locations gathered across limited spatial extents and analyzed using resource selection functions (RSFs) or spatially extensive locational data without individual resolution typically analyzed using species distribution models. Both analytical methodologies have certain desirable features, but analyses that combine individual- and population-level inference with flexible non-linear functions may provide improved predictions while accounting for individual variation. Here, we describe how RSFs can be fit using hierarchical generalized additive models (HGAMs) using widely available software, providing a means to explore individual variation in habitat associations and to generate species distribution maps. We used GPS tracking data from golden eagles Aquila chrysaetos from across eastern North America with four environmental predictors to generate monthly distribution models. We considered three model structures that assumed different amounts of individual variation in the functional relationship between predictors and habitat use and used k-fold cross-validation to compare model performance. Models accounting for individual variability in shape and smoothness of functional responses performed best. Eagles exhibited the least amount of individual variation in response to land cover variables during winter months, with most individuals more closely adhering to the population-level trend. During the summer months, eagles exhibited more substantial individual variation in shape and smoothness of the functional relationships, suggesting some need to account for individual variation in eagle habitat use for both inferential and predictive purposes, during this time of year. Because they allow users to blend flexible functions with random effects structures and are well-supported by a variety of software platforms, we believe that HGAMs provide a useful addition to the suite of analyses used for modeling habitat associations or predicting species distributions.

54 ENVIRONMENTAL SCIENCES↗

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange

In this report, electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact exchange or hybrid functionals are associated with large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Though orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use gradient expansion of the kinetic energy, nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C 4 H 2 , C 4 N 2 and C 3 O 2 . We show that by using data from model one-dimensional KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems as well as electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Archetype-based Redshift Estimation for the Dark Energy Spectroscopic Instrument Survey

We present a computationally efficient galaxy archetype-based redshift estimation and spectral classification method for the Dark Energy Survey Instrument (DESI) survey. The DESI survey currently relies on a redshift fitter and spectral classifier using a linear combination of principal component analysis–derived templates, which is very efficient in processing large volumes of DESI spectra within a short time frame. However, this method occasionally yields unphysical model fits for galaxies and fails to adequately absorb calibration errors that may still be occasionally visible in the reduced spectra. Our proposed approach improves upon this existing method by refitting the spectra with carefully generated physical galaxy archetypes combined with additional terms designed to absorb data reduction defects and provide more physical models to the DESI spectra. We test our method on an extensive data set derived from the survey validation (SV) and Year 1 (Y1) data of DESI. Our findings indicate that the new method delivers marginally better redshift success for SV tiles while reducing catastrophic redshift failure by 10%–30%. At the same time, results from millions of targets from the main survey show that our model has relatively higher redshift success and purity rates (0.5%–0.8% higher) for galaxy targets while having similar success for QSOs. These improvements also demonstrate that the main DESI redshift pipeline is generally robust. Additionally, it reduces the false-positive redshift estimation by 5%–40% for sky fibers. We also discuss the generic nature of our method and how it can be extended to other large spectroscopic surveys, along with possible future improvements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Similarity Metric for Data Optimization and Efficient Training of Reactive Machine Learning Force Fields for Hydrocarbon Radiolysis

Radiolysis is a common approach to sterilize polymers, chemically modify them for upcycling, and accelerate their decomposition for recycling purposes. Reactive molecular dynamics (MD) simulations provide a powerful tool to generate atomic-level trajectories of the reactive processes and quantify radiolytic chemical degradation pathways. For this, machine learning (ML) surrogate models for reactive force fields with quantum mechanical accuracy are now widely used, which require ML training data sets that can provide information on atomic environments for target chemical systems. However, radiolysis chemistry can be highly complex and diverse, which poses significant challenges for generating training data to parametrize ML models. In this regard, we developed a method for optimizing the training data set using a cosine similarity metric to help guide training set selection for radiolysis of polyethylene, a model hydrocarbon polymer, as well as to enhance the transferability of our reactive ML force field (MLFF) to a variety of molecular and polymeric systems. Our approach performs atom-by-atom comparisons between local atomic environments to pinpoint important data points associated with rare and localized events, such as radiolysis damage within structures. We apply this approach to train the Chebyshev Interaction Model for Efficient Simulation (ChIMES) MLFF model, which expresses the atomic interaction potentials in terms of linear combinations of many-body Chebyshev polynomials. We first show that our method can reduce our training set size by ∼70% while improving overall accuracy compared to more standard MD model fitting approaches. We then validate our optimum model against diverse hydrocarbon simulation data, including simple alkanes and systems with unsaturated carbon bonds, over a wide range of thermodynamic conditions. Finally, we use our ChIMES model to perform MD simulations of radiolytic damage with large-scale systems that help avoid system size effects. Overall, our approach yields an MD force field that retains most of the accuracy of the underlying quantum method while yielding many orders of improvement in computational efficiency. In conclusion, our efforts will have impact on future hydrocarbon polymer radiolysis studies, where the chemical details of the polymer–radiation interactions can have a strong effect on the resulting products observed in experiments.

Hydrocarbons↗

Autodifferentiable Spectrum Model for High-dispersion Characterization of Exoplanets and Brown Dwarfs

We present an autodifferentiable spectral modeling of exoplanets and brown dwarfs. This model enables a fully Bayesian inference of the high-dispersion data to fit the ab initio line-by-line spectral computation to the observed spectrum by combining it with the Hamiltonian Monte Carlo in recent probabilistic programming languages. An open-source code, ExoJAX, developed in this study, was written in Python using the GPU/TPU compatible package for automatic differentiation and accelerated linear algebra, JAX. We validated the model by comparing it with existing opacity calculators and a radiative transfer code and found reasonable agreements for the output. As a demonstration, we analyzed the high-dispersion spectrum of a nearby brown dwarf, Luhman 16 A, and found that a model including water, carbon monoxide, and H 2 /He collision-induced absorption was well fitted to the observed spectrum (R = 10 5 and 2.28-2.30 μm). As a result, we found that T0 = 1295$^{-32}_{+35}$ K at 1 bar and C/O = 0.62 ± 0.03, which is slightly higher than the solar value. This work demonstrates the potential of a full Bayesian analysis of brown dwarfs and exoplanets as observed by high-dispersion spectrographs and also directly imaged exoplanets as observed by high-dispersion coronagraphy.

79 ASTRONOMY AND ASTROPHYSICS↗

Disentangling the Impacts of Microtopography and Shrub Distribution on Snow Depth in a Subarctic Watershed: Toward a Predictive Understanding of Snow Spatial Variability

Snow plays a critical role in carbon cycling, vegetation dynamics, and permafrost hydrology at high latitudes by influencing surface energy exchange. Predicting snow distribution patterns is essential for understanding the evolution of Arctic ecosystems, yet scaling process-level knowledge to landscape predictions remains challenging. Here, we analyze snow depth (2019 and 2022), terrain elevation, and vegetation height from a watershed on the Seward Peninsula, Alaska, to examine how topography and shrubs shape snow redistribution across spatial scales. We find that snow depth is strongly coupled to terrain at scales below ∼60 m but becomes increasingly decoupled at larger scales. The topographic model of snow depth variation, which transforms terrain data to align with these scale-dependent snow patterns, is well correlated with local snow depth variations (linear fit R 2 > 0.5 for 85% of 100-m patches). A machine learning reconstruction of shrub canopy snow trapping reveals a simple exponential relationship between canopy structure and snow accumulation ( R 2 = 0.59), highlighting the combined influence of topography and vegetation on snow distribution. Together, these empirical relationships capture much of the observed snow variability in the watershed ( R 2 = 0.49, root mean square error (RMSE) = 30 cm), though systematic limitations persist in areas of strong scour and at coarser scales where wind-terrain interactions are more complex. These findings provide a framework for more efficient snow depth prediction and offer insights to improve snow-vegetation feedback representation in Earth System Models.

54 ENVIRONMENTAL SCIENCES↗

Identification of Novel Genomic Associations and Gene Candidates for Grain Starch Content in Sorghum

Starch accumulated in the endosperm of cereal grains as reserve energy for germination serves as a staple in human and animal nutrition. Unraveling genetic control for starch metabolism is important for breeding grains with high starch content. In this study, we used a sorghum association panel with 389 individuals and 141,557 single nucleotide polymorphisms (SNPs) to fit linear mixed models (LMM) for identifying genomic regions and potential candidate genes associated with starch content. Three associated genomic regions, one in chromosome (chr) 1 and two novel associations in chr-8, were identified using combination of LMM and Bayesian sparse LMM. All significant SNPs were located within protein coding genes, with SNPs ∼ 52 Mb of chr-8 encoding a Casperian strip membrane protein (CASP)-like protein (Sobic.008G111500) and a heat shock protein (HSP) 90 (Sobic.008G111600) that were highly expressed in reproductive tissues including within the embryo and endosperm. The HSP90 is a potential hub gene with gene network of 75 high-confidence first interactors that is enriched for five biochemical pathways including protein processing. The first interactors of HSP90 also showed high transcript abundance in reproductive tissues. The candidates of this study are likely involved in intricate metabolic pathways and represent candidate gene targets for source-sink activities and drought and heat stress tolerance during grain filling.

genomics↗

Combined Neyman–Pearson chi-square: An improved approximation to the Poisson-likelihood chi-square

We describe an approximation to the widely-used Poisson-likelihood chi-square using a linear combination of Neyman’s and Pearson’s chi-squares, namely “combined Neyman–Pearson chi-square” ($X^2_{CNP}$). Through analytical derivations and toy model simulations, we show that leads to a significantly smaller bias on the best-fit model parameters compared to those using either Neyman’s or Pearson’s chi-square. When the computational cost of using the Poisson-likelihood chi-square is high, $X^2_{CNP}$ provides a good alternative given its natural connection to the covariance matrix formalism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Quantification of Native Lignin Structural Features with Gel–Phase 2D–HSQC 0 Reveals Lignin Structural Changes During Extraction

Our ability to study and valorize the lignin fraction of biomass is hampered by the fundamental and still unmet challenge of precisely quantifying native lignin's structural features. Here, we developed a rapid elevated-temperature 1 H– 13 C Heteronuclear Single-Quantum Coherence Zero (HSQC 0 ) NMR method that enables this precise quantification of native lignin structural characteristics even with whole plant cell wall (WPCW) NMR spectroscopy, overcoming fast spin relaxation in the gel phase. We also formulated a Gaussian fitting algorithm to perform automatic and reliable spectral integration. By combining HSQC 0 measurements with yield measurements following depolymerisation, we can confirm the combinatorial nature of radical coupling reactions during biosynthesis leading to a random sequential organization of linkages within a largely linear lignin chain. Such analyses illustrate how this analytical method can greatly facilitate the study of native lignin structure, which can then be used for fundamental studies or to understand lignin depolymerization methods like reductive catalytic fractionation or aldehyde-assisted fractionation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantification of Native Lignin Structural Features with Gel–Phase 2D–HSQC 0 Reveals Lignin Structural Changes During Extraction

Our ability to study and valorize the lignin fraction of biomass is hampered by the fundamental and still unmet challenge of precisely quantifying native lignin's structural features. Here, we developed a rapid elevated-temperature 1 H– 13 C Heteronuclear Single-Quantum Coherence Zero (HSQC 0 ) NMR method that enables this precise quantification of native lignin structural characteristics even with whole plant cell wall (WPCW) NMR spectroscopy, overcoming fast spin relaxation in the gel phase. We also formulated a Gaussian fitting algorithm to perform automatic and reliable spectral integration. By combining HSQC 0 measurements with yield measurements following depolymerisation, we can confirm the combinatorial nature of radical coupling reactions during biosynthesis leading to a random sequential organization of linkages within a largely linear lignin chain. Such analyses illustrate how this analytical method can greatly facilitate the study of native lignin structure, which can then be used for fundamental studies or to understand lignin depolymerization methods like reductive catalytic fractionation or aldehyde-assisted fractionation.

09 BIOMASS FUELS↗

Long-term sinking of nuclear waste canisters in salt formations by low-stress creep at high temperature

Abstract Rock salt has a self-sealing capacity, low permeability, and high thermal conductivity, making it a potential host for heat-generating nuclear waste. The feasibility of nuclear waste disposal within salt formations has been investigated mostly for small-sized canisters. Geologic disposal of larger-sized canisters originally designed for spent fuel storage and transportation has lately been examined as a cost-effective alternative. This raises questions about their long-term vertical movement due to their weight and high decay heat. Low-stress creep governs this movement; however, most salt constitutive models do not incorporate it. In this paper, the Norton and the WIPP creep models are compared with the Lux/Wolters/Lerche (LWL) model and a simpler model that combines linear and Norton creep laws (named combined creep model). The LWL and combined creep models consider pressure solution creep, though all incorporate dislocation creep. The models are first applied to creep tests under various stress levels. The LWL and the combined creep models results fit the experimental data well in both high and low stress ranges, whereas the Norton and WIPP models results only fit in higher-stress ranges. The different models are further applied for analyzing long-term canister movement. A sinking rate of $$-4.4\times 10^{-7}$$ - 4.4 × 10 - 7 mm/year was predicted using the Norton and WIPP models versus $$-2.1\times 10^{-2}$$ - 2.1 × 10 - 2 mm/year and $$-3.1\times 10^{-2}$$ - 3.1 × 10 - 2 mm/year using the LWL and the combined creep models, respectively. This comparative study confirms that creep models calibrated exclusively against high-deviatoric stress data might result in an inaccurate estimation of waste packages sinking rate in salt formations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Visualizing Charge Transport and Nanoscale Electrochemistry by Hyperspectral Kelvin Probe Force Microscopy

Charge-transport and electrochemical processes are heavily influenced by the local microstructure. Kelvin probe force microscopy (KPFM) is a widely used technique to map electrochemical potentials at the nanometer scale; however, it offers little information on local charge dynamics. In this study, we implement a hyperspectral KPFM approach for spatially mapping bias-dependent charge dynamics in timescales ranging from the sub-millisecond to the second regime. As a proof of principle, we investigate the role mobile surface charges play in a three-unit-cell LaAlO 3 /SrTiO 3 oxide heterostructure. We explore machine learning approaches to assist with visualization, pattern recognition, and interpretation of the information-rich data sets. Linear unmixing methods reveal hidden bias-dependent interfacial processes, most likely water splitting, which are essentially unnoticed by functional fitting of the dynamic response alone. Hyperspectral KPFM will be beneficial for investigating nanoscale charge transport and local reactivity in systems involving a possible combination of electronic, ionic, and electrochemical phenomena.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Environmental controls on the light use efficiency of terrestrial gross primary production

Abstract Gross primary production (GPP) by terrestrial ecosystems is a key quantity in the global carbon cycle. The instantaneous controls of leaf‐level photosynthesis are well established, but there is still no consensus on the mechanisms by which canopy‐level GPP depends on spatial and temporal variation in the environment. The standard model of photosynthesis provides a robust mechanistic representation for C 3 species; however, additional assumptions are required to “scale up” from leaf to canopy. As a consequence, competing models make inconsistent predictions about how GPP will respond to continuing environmental change. This problem is addressed here by means of an empirical analysis of the light use efficiency (LUE) of GPP inferred from eddy covariance carbon dioxide flux measurements, in situ measurements of photosynthetically active radiation (PAR), and remotely sensed estimates of the fraction of PAR (fAPAR) absorbed by the vegetation canopy. Focusing on LUE allows potential drivers of GPP to be separated from its overriding dependence on light. GPP data from over 100 sites, collated over 20 years and located in a range of biomes and climate zones, were extracted from the FLUXNET2015 database and combined with remotely sensed fAPAR data to estimate daily LUE. Daytime air temperature, vapor pressure deficit, diffuse fraction of solar radiation, and soil moisture were shown to be salient predictors of LUE in a generalized linear mixed‐effects model. The same model design was fitted to site‐based LUE estimates generated by 16 terrestrial ecosystem models. The published models showed wide variation in the shape, the strength, and even the sign of the environmental effects on modeled LUE. These findings highlight important model deficiencies and suggest a need to progress beyond simple “goodness of fit” comparisons of inferred and predicted carbon fluxes toward an approach focused on the functional responses of the underlying dependencies.

54 ENVIRONMENTAL SCIENCES↗

Impact of U-10Mo HALEU fuel element tolerances on the Massachusetts Institute of Technology reactor safety and operational performance – Thermal hydraulics

The U.S. is coordinating efforts for the conversion of six U.S. High Performance Research Reactors (USHPRR) including one critical facility from highly enriched uranium (HEU) to low-enriched uranium (LEU). In order to continue the mission of these reactors, including the Massachusetts of Institute of Technology Reactor (MITR), and achieve similar performance, high-assay low-enriched uranium (HALEU) with a high-density metallic alloy of uranium with 10 wt% molybdenum (U-10Mo) is being evaluated. The impact of the fabrication specification and tolerances was assessed following the preliminary design of the MITR LEU fuel elements using the U-10Mo monolithic alloy. This research focuses on the analysis of fabrication specification impact on thermal hydraulics (TH) characteristic of the MITR LEU core as a function of the variation of the relevant fuel specification parameters (e.g., coolant channel gap thickness, fuel plate thickness, etc.). The analyses are performed based on an all-fresh LEU fuel conversion plan identified in a preliminary safety analysis report submitted to the Nuclear Regulatory Commission. The reactor power margin to the onset of nucleate boiling (ONB) is assessed under the limiting safety system settings (LSSS), where a scram occurs, to ensure there is sufficient margin to the reactor safety limit, which is defined by the onset of flow instability that occurs after the ONB. The best estimate plus uncertainty approach is employed to analyze this TH characteristic, which yields realistic results while maintaining adequate conservatism, utilizing a statistical uncertainty propagation method with the STAT7 code. The TH characteristic is analyzed as a function of the variability of the specification parameters resulting from the fabrication process. The main findings of this study show that the MITR core can meet the TH safety and operational requirements at the all-LEU initial core startup (cycle 1), selected transition cycles (most reactive cycle and most limiting cycle: cycle 3 and 5, respectively) and equilibrium (cycle 14) cores under all limiting fabrication parameter combinations considered. In addition, the analyses show that the dependency of the core power margin to ONB on those specification parameters that have the most direct impact on TH performance is non-linear but monotonically decreasing within the specification tolerances. The third order polynomial fit curves are reported in detail for selected limiting cases and can serve as a powerful tool for future MITR fuel management in cases such as when HALEU supply is established that may allow additional cycle length or other operational benefits.

Conversion↗

In-flight polarization angle calibration for LiteBIRD: blind challenge and cosmological implications

We present a demonstration of the in-flight polarization angle calibration for the JAXA/ISAS second strategic large class mission, LiteBIRD, and estimate its impact on the measurement of the tensor-to-scalar ratio parameter, r, using simulated data. We generate a set of simulated sky maps with CMB and polarized foreground emission, and inject instrumental noise and polarization angle offsets to the 22 (partially overlapping) LiteBIRD frequency channels. Our in-flight angle calibration relies on nulling the EB cross correlation of the polarized signal in each channel. This calibration step has been carried out by two independent groups with a blind analysis, allowing an accuracy of the order of a few arc-minutes to be reached on the estimate of the angle offsets. Both the corrected and uncorrected multi-frequency maps are propagated through the foreground cleaning step, with the goal of computing clean CMB maps. We employ two component separation algorithms, the Bayesian-Separation of Components and Residuals Estimate Tool (B-SeCRET), and the Needlet Internal Linear Combination (NILC). We find that the recovered CMB maps obtained with algorithms that do not make any assumptions about the foreground properties, such as NILC, are only mildly affected by the angle miscalibration. However, polarization angle offsets strongly bias results obtained with the parametric fitting method. Once the miscalibration angles are corrected by EB nulling prior to the component separation, both component separation algorithms result in an unbiased estimation of the r parameter. While this work is motivated by the conceptual design study for LiteBIRD, its framework can be broadly applied to any CMB polarization experiment. In particular, the combination of simulation plus blind analysis provides a robust forecast by taking into account not only detector sensitivity but also systematic effects.

79 ASTRONOMY AND ASTROPHYSICS↗

Construction of linearly independent non-orthogonal AGP states

We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. Furthermore, this greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Active learning for robust, high-complexity reactive atomistic simulations

Machine learned reactive force fields based on polynomial expansions have been shown to be highly effective for describing simulations involving reactive materials. Nevertheless, the highly flexible nature of these models can give rise to a large number of candidate parameters for complicated systems. In these cases, reliable parameterization requires a well-formed training set, which can be difficult to achieve through standard iterative fitting methods. In this paper, we present an active learning approach based on cluster analysis and inspired by Shannon information theory to enable semi-automated generation of informative training sets and robust machine learned force fields. The use of this tool is demonstrated for development of a model based on linear combinations of Chebyshev polynomials explicitly describing up to four-body interactions, for a chemically and structurally diverse system of C/O under extreme conditions. We show that this flexible training database management approach enables development of models exhibiting excellent agreement with Kohn–Sham density functional theory in terms of structure, dynamics, and speciation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗