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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 361 records · Page 20

A Markov chain Monte Carlo (MCMC) Bayesian inference approach to analyze apparent activation barriers and reaction orders from microreactor data

Statistical analysis of steady-state catalytic kinetic data is often limited by data sparsity due to the slow pace at which the data is collected. Data sparsity and limitations in statistical analysis make it difficult to differentiate between mechanistic models and catalytic sites. A Bayesian inference tool is reported for catalysis researchers to estimate error in the determination of reaction orders from steady state microreactor data. The benefits of a Bayesian inference approach are discussed, as an alternative to the more common frequentist approach. The approach incorporates prior knowledge of the system and the data collected to form an error estimate on reaction orders. We investigated the effects of three distinct data treatments—individual fitting of trials, pooled analysis, and constrained regression methods—on the precision and uncertainty of reaction order determinations. To assess the robustness of our findings, we conducted sensitivity analyses to evaluate the influence of Bayesian parameters on uncertainty estimation. Additionally, we utilized synthetic data to illustrate how data quality impacts the precision of uncertainty assessments. We show Bayesian analysis can obtain a more precise estimation of error with a sparse data set than a frequentist analysis. Finally, this work provides strong evidence that the adoption of Bayesian analysis of kinetic data may help researchers make more precise arguments as to the strength of their evidence for a particular mechanistic hypothesis, or in comparing across different catalysts.

42 ENGINEERING↗

Toward a Machine Learning Approach to Interpreting X-ray Spectra of Trace Impurities by Converting XANES to EXAFS

The fact that the photoabsorption spectrum of a material contains information about the atomic structure, commonly understood in terms of multiple scattering theory, is the basis of the popular extended X-ray absorption spectroscopy (EXAFS) technique. How much of the same structural information is present in other complementary spectroscopic signals is not obvious. Here we use a machine learning approach to demonstrate that within theoretical models that accurately predict the EXAFS signal, the extended near-edge region does indeed contain the EXAFS-accessible structural information. We do this by exhibiting deep operator neural networks (DeepONets) that have learned the relationship between the extended and near edge portions of the X-ray absorption spectrum to predict the former from the latter. We find that we can accurately predict the EXAFS spectrum between 6 and 14 Å –1 from the first 6 Å –1 (≈100 eV) of the absorption spectrum of Cu 2 + substitutional defects in the Fe 3+ mineral hematite (α-Fe 2 O 3 ). This surprising finding implies that theoretical analyses of X-ray absorption spectra could be implemented that extract the same conclusions as high-quality EXAFS studies from spectra collected over a much smaller range of photon energies. This relaxes a host of experimental limitations related to the X-ray source and measurement sample, including collection time, minimum dopant concentration, source brilliance, and energy range. We describe the theoretical data sets and DeepONet construction and show that the resulting DeepONets produce EXAFS that recovers linear combination fits to experimental data with accuracy approaching the original ab initio calculations. We discuss the implications of our findings for minor constituent characterization and for understanding the information content of spectroscopic data more broadly, including how this approach might be applied to measured experimental spectra. In conclusion, to encourage similar efforts, the simulated X-ray spectra, machine learning, and fitting code are publicly available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Leveraging Large Language Models for Understanding Fundamental Principles of Catalysis

Heterogeneous catalysis presents a distinct challenge for artificial intelligence (AI). Data sets are often small and inconsistently reported, catalyst representations are not standardized, and extracting fundamental knowledge requires integrating performance data, spectroscopic characterizations, and mechanistic models across multiple scales. Language offers a unifying representation across these modalities, making catalysis well suited for leveraging large language models (LLMs). By standardizing how catalytic data is represented, LLMs make dispersed experimental results more accessible to downstream statistical modeling. In this perspective, we focus our discussion around three opportunities where LLMs can significantly contribute to catalysis: (1) text to properties; (2) text to structure; and (3) text to mechanistic models. The discussion is followed by a perspective section on LLM-readiness of data, aligning LLM outputs with scientific correctness, and bridging lab-scale discovery to industrial deployment. Across each area, the most productive applications couple dispersed chemical knowledge with physics-grounded validation to produce verifiable hypotheses and actionable representations.

Catalysts↗

Search for heavy long-lived charged particles with level-1 trigger scouting data from proton-proton collisions at $\sqrt{s} = 13.6$ TeV

A search for heavy long-lived charged particles at the LHC is presented. Particles interacting with the CMS muon detector across several bunch crossings are searched for using a data sample of proton-proton collisions at $\sqrt{s}$ = 13.6 TeV collected with the CMS detector in 2024, corresponding to an integrated luminosity of 3.7 fb$^{-1}$. This is the first search relying on the novel level-1 trigger scouting data set collected without any trigger selection, allowing correlations between bunch crossings to be analyzed. The results are interpreted as upper limits on the cross sections of several benchmark processes with pair production of heavy long-lived charged particles. Upper limits on the fiducial cross section of a heavy long-lived charged particle with $p_\mathrm{T}$$\gt$ 500 GeV and $\lvertη\rvert$$\lt$ 0.83 are also set in different ranges of $β=v/c$. This analysis is a crucial proof of concept for the level-1 trigger data scouting system and complements existing searches for heavy long-lived charged particles by extending the sensitivity to lower $β$ values.

CMS↗

The Snow Albedo Evolution (SALVO) Campaign at the North Slope of Alaska Field Campaign Report

The springtime surface-albedo transition in the Alaskan Arctic, along with the forces that determine its duration and nature, was the focus of the Snow ALbedo eVOlution (SALVO) campaign. The SALVO team investigated the reasons and durations of the stages of spring melt, during which albedo values decrease from 0.8 to 0.1, signifying the year’s largest and most significant radiative energy change. SALVO II (2022, 2024) built on findings from the successful SALVO I (2019) melt season campaign and previous research on the melt transition period conducted by Grenfell and Perovich (2004). SALVO used the ARM NSA observatory, thus aligning with a core principle of the ARM Decadal Vision to “provide comprehensive and impactful field measurements to support scientific advancement of atmospheric process understanding.” SALVO fieldwork was conducted in the spring near the ARM NSA Central Facility in Utqiagvik, Alaska (Figure 1). Comprehensive data sets were collected in 2019, 2022, and 2024, which included spectral and broadband albedos, snow and meltwater depths, snow stratigraphy, snow grain size data, and aerial imagery. In April of each project year, before the snow began to melt, we established survey lines at three or four locations: inland tundra at NSA E12, coastal tundra at the NSA C1 site, Elson Lagoon, and offshore on the Chukchi Sea sea ice (2022 only). We set up a 200-meter-long line, marked every five meters, to enable repeated measurements of surface albedo and snow depth at each location. During most site visits, the SALVO II team dug at least one snow pit to assess the characteristics of the vertical snow layers, including the types and sizes of snow grains, snow density, and the distribution of liquid water. We evaluated the characteristics of flowing or pooled water at the bottom of the snowpack. Watching snow melt in the Arctic has been compared by some to being as exciting as watching paint dry, but it is far more exciting and dynamic than that. Initially, changes happen slowly while the snow cover remains above 80%, but then reductions in the albedo of the landscape, from about 0.8 to 0.4, combined with rising spring temperatures, begin to accelerate the melt. It happens so quickly that no matter how hard the field team works, they cannot keep up with documenting the changes. At first, liquid water is scarce—only a few wet layers of snow in the snowpack. But then, water becomes ubiquitous, transporting melt energy and creating an extremely heterogeneous albedo and melt landscape. At the end of each field season, the SALVO team is exhausted, relieved to see the snow gone, and joyful to play in the melt ponds on the sea ice under the midnight sun. Overall, the 2024 SALVO field campaign was a highlight, reflecting numerous lessons learned from 2019 and 2022. Daily measurements were taken more than 10 times at each site, resulting in a comprehensive time series of snow conditions and albedo. The team deployed using snowmachines and then on foot when snowmachine travel was no longer permitted on the melting tundra. Instrument mounts and packaging were optimized for quick deployment, regardless of the mode of transportation.

54 ENVIRONMENTAL SCIENCES↗

Measuring the Conditional Luminosity and Stellar Mass Functions of Galaxies by Combining the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 Data

In this investigation, we leverage the combination of the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 data sets to estimate the conditional luminosity functions and conditional stellar mass functions (CLFs and CSMFs) of galaxies across various halo mass bins and redshift ranges. To support our analysis, we utilize a realistic DESI mock galaxy redshift survey (MGRS) generated from a high-resolution Jiutian simulation. An extended halo-based group finder is applied to both MGRS catalogs and DESI observation. By comparing the r- and z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived using both photometric and spectroscopic data, we quantified the impact of photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in the low-redshift bin at the low-luminosity/mass end. By conducting prior evaluations of the group finder using MGRS, we successfully obtain a set of CLF and CSMF measurements from observational data. We find that at low redshift, the faint-end slopes of CLFs and CSMFs below ~10 9 h –2 L ⊙ (or h –2 M ⊙ ) evince a compelling concordance with the subhalo mass functions. After correcting the cosmic variance effect of our local Universe following Chen et al., the faint-end slopes of the LFs/SMFs turn out to also be in good agreement with the slope of the halo mass function.

79 ASTRONOMY AND ASTROPHYSICS↗

Dark Energy Survey Year 3 Results: Cosmological Constraints from Cluster Abundances, Weak Lensing, and Galaxy Clustering

Galaxy clusters provide a unique probe of the late-time cosmic structure and serve as a powerful independent test of the $\Lambda$CDM model. This work presents the first set of cosmological constraints derived with ~16,000 optically selected redMaPPer clusters across nearly 5,000 $\rm{deg}^2$ using DES Year 3 data sets. Our analysis leverages a consistent modeling framework for galaxy cluster cosmology and DES-Y3 joint analyses of galaxy clustering and weak lensing (3x2pt), ensuring direct comparability with the DES-Y3 3x2pt analysis. We obtain constraints of $S_8 = 0.864 \pm 0.035$ and $\Omega_{\rm{m}} = 0.265^{+0.019}_{-0.031}$ from the cluster-based data vector. We find that cluster constraints and 3x2pt constraints are consistent under the $\Lambda$CDM model with a Posterior Predictive Distribution (PPD) value of $0.53$. The consistency between clusters and 3x2pt provides a stringent test of $\Lambda$CDM across different mass and spatial scales. Jointly analyzing clusters with 3x2pt further improves cosmological constraints, yielding $S_8 = 0.811^{+0.022}_{-0.020}$ and $\Omega_{\rm{m}} = 0.294^{+0.022}_{-0.033}$, a $24\%$ improvement in the $\Omega_{\rm{m}}-S_8$ figure-of-merit over 3x2pt alone. Moreover, we find no significant deviation from the Planck CMB constraints with a probability to exceed (PTE) value of $0.6$, significantly reducing previous $S_8$ tension claims. Finally, combining DES 3x2pt, DES clusters, and Planck CMB places an upper limit on the sum of neutrino masses of $\sum m_\nu < 0.26$ eV at 95% confidence under the $\Lambda$CDM model. These results establish optically selected clusters as a key cosmological probe and pave the way for cluster-based analyses in upcoming Stage-IV surveys such as LSST, Euclid, and Roman.

79 ASTRONOMY AND ASTROPHYSICS↗

Opportunistic Short‐Term Water Uptake Dynamics by Subalpine Trees Observed via In Situ Water Isotope Measurements

Abstract Variations in tree water sources are important to understand in semi‐arid ecosystems because climatic shifts towards lower snowpack and increased drought affect water availability in subalpine forests of the western US. Here, we use daily in situ measurements of stable isotopes ( 2 H & 18 O) in soil and tree stem water, soil matric potential and sap flow to study tree water uptake dynamics. We instrumented three soil profiles down to 90 cm, as well as three aspen and engelmann spruce trees near Gothic, Colorado, in the East River watershed. We observed the fate of natural isotopic variations in rainfall, soil, and plants from June to October 2022, and in August 2023 we conducted a 2 H labeled irrigation experiment. Our observations showed that all studied aspen trees compensated for water scarcity in the shallow soil by shifting the dominant water source at 60(±20) cm to ⅔ of uptake from 90 cm within a few days of a dry period. Both species relied on snowmelt stored in the subsoil to sustain transpiration. Intense rainfall caused the plant water uptake to shift partially to top soil layers within 2 days. Spruce transpiration was lower and relied more on snowmelt, because rainfall infiltration was low in the spruce stand due to high canopy interception. Our findings highlight the important role of snowmelt stored in the deep soil layers for subalpine forest drought response and the dominant fate of monsoonal rainfall to become transpiration rather than recharging groundwater and streams in the Upper Colorado River. Plain Language Summary There is a need to understand how trees in mountainous regions respond to dry conditions that lead to water scarcity, because climate projections suggest that such conditions will become more frequent in the future. Here we present a novel data set of measurements of daily stable isotopes of water across soil profiles and in tree stems of aspen and spruce. Our data show that when the upper soil dried out, aspen trees shifted to using water from deeper layers (beneath 60 cm) to keep transpiring. For spruce trees the uptake pattern is less clear, but both types of trees mainly used snowmelt stored in the deeper soil layers to survive the dry summer. After heavy rain, aspen and spruce trees switched to using water from the top 20 cm of soil. However, for spruce, only some rain reached the soil because the dense tree canopy intercepted it, so spruce trees stayed more dependent on snowmelt and used less water overall. This study shows how important deep snowmelt water is for helping forests survive dry periods and suggests that most summer rain is quickly used by trees rather than replenishing streams and groundwater in the headwaters of the Colorado River. Key Points Tree water resources changed within a few days from snow dominated to higher share of rainfall as soils wetted up after a dry period Compensatory plant water uptake by aspen from the deep layer (90 cm), while uptake from soil depths that became drier (60 cm) declined Strong differences between water sources and availability beneath aspen and spruce, respectively

Sprenger, Matthias↗

Development of a deep potential model for F and CF 2 etching of Si and SiO 2

An understanding of plasma-surface interactions at increasingly smaller scales is invaluable for the development of novel technologies and processing techniques. Molecular dynamics (MD) simulations can provide insights into atomic-scale interactions, though they are restricted by the availability of interatomic potentials. Machine learning methods, such as Deep Potential Molecular Dynamics (DeepMD), provide a systematic framework for the development of accurate and flexible ab initio-based models. In this work, we develop DeepMD models for the ion-enhanced etching of Si and SiO 2 by F and CF 2 radicals. We employ an active learning process to expand the data set on which the model is trained and demonstrate its effect on the model accuracy. The DeepMD results are compared to data from classical MD simulations and experiments. Physical sputtering yields of SiO 2 by Ar + ions show good agreement with previous simulation results using conventional interatomic potentials, though the predicted depth profiles are different. Etching yields are calculated as a function of ion energy and neutral to ion flux ratio for the Ar + ion-enhanced etching of SiO 2 and Si by F atoms, as well as for etching of SiO 2 by CF 2 radicals, showing reasonable agreement with experimental data. Finally, an ion-enhanced surface kinetic model is fitted to the DeepMD etch yields, and the fitted parameters are compared to quantities computed directly from DeepMD simulations. This study illustrates how molecular dynamics simulations using machine learning potentials can provide an accurate model of etching processes relevant to device manufacturing.

Kounis-Melas, Andreas [Princeton Univ., NJ (United↗

Deep Learning Advances Arctic River Water Temperature Predictions

The accelerated warming in the Arctic poses serious risks to freshwater ecosystems by altering streamflow and river thermal regimes. However, limited research on Arctic River water temperatures exists due to data scarcity and the absence of robust methodologies, which often focus on large, major river basins. To address this, we leveraged the newly released, extensive AKTEMP data set and advanced machine learning techniques to develop a Long Short-Term Memory (LSTM) model. By incorporating ERA5-Land reanalysis data and integrating physical understanding into data-driven processes, our model advanced river water temperature predictions in ungauged, snow- and permafrost-affected basins in Alaska. Our model outperformed existing approaches in high-latitude regions, achieving a median Nash-Sutcliffe Efficiency of 0.95 and root mean squared error of 1.0°C. The LSTM model learned air temperature, soil temperature, solar radiation, and thermal radiation—factors associated with energy balance—were the most important drivers of river temperature dynamics. Soil moisture and snow water equivalent were highlighted as critical factors representing key processes such as thawing, melting, and groundwater contributions. Glaciers and permafrost were also identified as important covariates, particularly in seasonal river water temperature predictions. Our LSTM model successfully captured the complex relationships between hydrometeorological factors and river water temperatures across varying timescales and hydrological conditions. This scalable and transferable approach can be potentially applied across the Arctic, offering valuable insights for future conservation and management efforts.

54 ENVIRONMENTAL SCIENCES↗

Deep Learning Reconstruction of Daily Soil CO 2 Efflux Reveals Biogeochemical Insights and Reduces Annual Estimate Uncertainty Despite Limited Daily Predictability

Soil CO 2 efflux is commonly measured monthly or seasonally, leaving daily dynamics poorly resolved and contributing to global estimation uncertainty. We trained a single Long Short-Term Memory (LSTM) model to predict daily soil CO 2 efflux across 82 globally distributed sites in COSORE, with 0.2%–46.9% daily data coverage from 2003 to 2020. Despite using far fewer sites than are typically used to train a single deep learning model, with observations biased toward temperate mesic sites, the LSTM model performed well at approximately one-third of sites, reconstructed nearly 2 decades of daily efflux, and outperformed commonly used approaches for estimating daily efflux when applied to the same data set. Performance was weakest at pronounced peaks and troughs and at non-temperate sites with <1.5 years of observations and irregular data patterns. Nevertheless, annual efflux from reconstructed daily data had <40% error even at underperforming sites, substantially improving estimates derived from monthly and seasonal sampling (maximum errors of 95% and 136%, respectively). Temperature sensitivity (Q 10 ) estimated from reconstructed daily predictions closely matched estimates from daily observations, whereas Q 10 values derived from monthly or seasonal observations deviated substantially, suggesting that coarse temporal sampling may contribute to uncertainty in reported Q 10 values. Consistent daily reconstructions further enabled trend analyses for well-performing, predominantly temperate sites and showed increasing soil CO 2 efflux at most sites from 2003 to 2020, with more variable summer trends. Despite limitations, these results demonstrate the potential of LSTM models to reconstruct daily soil CO 2 efflux and reduce estimation uncertainties from sparse observations.

Smykalov, Valerie [Pennsylvania State University, ↗

DUNE – Simulation Validation of Fermilab Detector Reconstruction

DUNE (Deep Underground Neutrino Experiment) is Fermilab’s flagship international experiment designed to study neutrinos by sending an intense beam from Illinois to detectors located 1,300 kilometers away at the Sanford Underground Research Facility (SURF) in South Dakota. To prepare for such a large-scale experiment, physicists develop detailed simulations to produce mock data sets which are analyzed by the CAFAna framework. During my internship, I developed software using the CAFAna framework to analyze simulated detector data and generated plots to make data trends easier to interpret and identify patterns. My analysis has uncovered inconsistencies in reconstructed neutrino tracks, duplicated reconstructed tracks causing sporadic spikes in the data, and unnatural differences in energy levels between interaction types. These analyses help verify that the improvements to detector simulations do not introduce unintended resolution errors and ensure proper reconstruction performance, supporting DUNE’s goal of making precise neutrino measurements and advancing the Department of Energy’s mission of fundamental scientific discovery.

Vershaw, Andre [Unlisted, US, IL; Fermilab] (ORCID↗

A Tutorial Set to Prepare for Science with the Vera C. Rubin Observatory

In this poster the Rubin Observatory's Community Science team (CST) presents its current suite of tutorials, which are designed to help people make use of simulated data sets in preparation for the upcoming Legacy Survey of Space and Time (LSST). We will show examples of the tutorial contents, provide custom learning modules for different astronomical fields, and describe the online environment for data analysis (the Rubin Science Platform; RSP). We will also supply a checklist for how to obtain an RSP account and access the tutorials. All are welcome to drop by the poster or the Rubin booth in the exhibit hall with questions.

79 ASTRONOMY AND ASTROPHYSICS↗

A Tutorial Set to Prepare for Science with the Vera C. Rubin Observatory

In this poster the Rubin Observatory's Community Science team (CST) presents its current suite of tutorials, which are designed to help people make use of simulated data sets in preparation for the upcoming Legacy Survey of Space and Time (LSST). We will show examples of the tutorial contents, provide custom learning modules for different astronomical fields, and describe the online environment for data analysis (the Rubin Science Platform; RSP). We will also supply a checklist for how to obtain an RSP account and access the tutorials. All are welcome to drop by the poster or the Rubin booth in the exhibit hall with questions.

79 ASTRONOMY AND ASTROPHYSICS↗

Modeling of the metal–insulator transition temperature in alio-valently doped VO 2 through symbolic regression

The correlated semiconductor vanadium dioxide (VO 2 ) exhibits an insulator–metal transition (IMT) near room temperature, which is of interest in various device applications. Precise IMT temperature control is crucial to determine the use cases across technologies such as thermochromic windows, actuators for robots or neuronal oscillators. Doping the cation or anion sites can modulate the IMT by several tens of degrees and control hysteresis. However, modeling the effects of control parameters (e.g., doping concentration, type of dopants) is challenging due to complex experimental procedures and limited data, hindering the use of traditional data-driven machine learning approaches. Symbolic regression (SR) can bridge this gap by identifying nonlinear expressions connecting key input parameters to target properties, even with small data sets. In this work, we develop SR models to capture the IMT trends in VO 2 influenced by different dopant parameters. Using experimental data from the literature, our study reveals a dual nature of the IMT temperature with varying tungsten (W) doping concentrations. The symbolic model captures data trends and accounts for experimental variability, providing a complementary approach to first-principles calculations. Our feature-driven analysis across a broader class of dopants informs selectivity and provides qualitative insights into tuning phase transition properties valuable for neuromorphic computing and thermochromic windows.

36 MATERIALS SCIENCE↗

Light Meson Spectroscopy with GlueX and Beyond

The GlueX experiment at Jefferson Lab was specifically designed for precision studies of the light-meson spectrum. For this purpose, a photon beam with energies up to 12 GeV is directed onto a liquid hydrogen target contained within a hermetic detector with near-complete neutral and charged particle coverage. Linear polarization of the photon beam with a maximum around 9 GeV provides additional information about the production process. In 2018, the experiment completed its first phase, recording data with a total integrated luminosity above 400 pb?1. We highlight a selection of results from this world-leading data set with emphasis on the search for light hybrid mesons. In the mean time, the detector underwent significant upgrades and is currently recording data with an even higher luminosity. The future plans of the GlueX experiment to explore the meson spectrum with unprecedented precision are summarized.

Austregesilo, Alexander↗

Using FIPD and OPTD to Benchmark Metallic Fuel Performance

This report serves as an introduction, tutorial, and benchmark specification for out-of-pile tests on metallic fuel. It introduces a new user to the EBR-II legacy fuel performance test program and the fast reactor fuel performance databases built to preserve the records. It then details the information stored in each database and how to find it. A benchmark specification is included for a small set of out-of-pile tests on U-10Zr fuel to function as a tutorial demonstrating how the legacy fuel performance data sets stored in the FIPD and OPTD databases can be used together to benchmark fuel performance models for steady-state and transient performance.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Neural Networks for Prediction of Complex Chemistry in Water Treatment Process Optimization

Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The effect of NN architecture on optimization is evaluated by optimizing hypothetical black-box desalination processes using a range of feed compositions from USGS brackish water data set, tracking the number of successful optimizations, and testing the impact of initial guess on the final solution. Our results clearly demonstrate that data generation and architecture impact NN accuracy and viability for use in equation-oriented optimization problems.

Dudchenko, Alexander V↗