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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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A New Paradigm for Observing and Modeling of Air-Sea Interactions to Advance Earth System Prediction

The protection of people, property, and environmental resources from extreme weather, seasonal patterns, and climate change drives the need for predictions of weather, ocean, and climate patterns that have skill and value at timescales longer than traditional 1-10-day forecasts, including outlooks spanning weeks to decades. Advancing Earth System Prediction (ESP) skill at this range of timescales requires improved observations, understanding, and modeling of the processes in the ocean boundary layer, the atmospheric boundary layer, and their interface. A new way of referring to this coupled system is the Air-Sea Transition Zone (ASTZ). The report that follows is framed by the paradigm that the ASTZ is a single entity that regulates the flow of energy and matter between the ocean and the atmosphere. The ASTZ is thus the medium through which the ocean and atmosphere respond to and influence one another across their often disparate scales of variability. ASTZ modeling, observing, and understanding needs are particularly acute because very few measurements exist over oceans, and even fewer span the entire ASTZ, even though oceans cover 70% of Earth’s surface and are the source of most of the rain and snow that falls on both the land and the oceans.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Novel Signatures Beyond the Standard Model: From Extreme Environments to Precision Measurements

Most of our universe is dark. It is dark literally—visible matter makes up only 5% of the energy density—and conceptually, as many outstanding questions remain unsolved. The discovery of particle dark matter would shed light on our dark universe and throw open a window on the highest energy scales. This research made progress toward dark matter and new particle searches in three ways. Extreme compact objects, such as black holes, neutron stars, and stellar cores, can parametrically increase the production rates of feebly interacting particles and yield observable signatures. Specifically, a process known as superradiance leads to exponential growth of the number of ultralight particles gravitationally bound to rotating black holes, and turns astrophysical black holes into particle detectors. This research broadened the scope of applicability of superradiance studies to particles with a wide range of interactions and masses, predicting multi messenger signals. When ultralight particles are produced as dark matter in the early universe, they can be detected directly in laboratory experiments. However, these feebly interacting particles lead to small signals that are inevitably difficult to tease out from backgrounds; their detection requires the theoretical development of unique signatures that can be searched for in low-noise experiments. Some dark matter particles could be detectable with thin film metamaterials combined with low noise single-photon detectors. This research develop the theoretical framework and supported experimental efforts for ambitious searches for a wider class of ultralight particles. Overall, the outcome of this theoretical particle physics program developed novel signatures of new dark matter particles, and thereby expanded the particle parameter space which can be explored with astrophysical observations and precision experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Variability-selected Intermediate-mass Black Hole Candidates in Dwarf Galaxies from ZTF and WISE

While it is difficult to observe the first black hole seeds in the early universe, we can study intermediate-mass black holes (IMBHs) in local dwarf galaxies for clues about their origins. In this paper we present a sample of variability-selected active galactic nuclei (AGN) in dwarf galaxies using optical photometry from the Zwicky Transient Facility (ZTF) and forward-modeled mid-IR photometry of time-resolved Wide-field Infrared Survey Explorer (WISE) co-added images. We found that 44 out of 25,714 dwarf galaxies had optically variable AGN candidates and 148 out of 79,879 dwarf galaxies had mid-IR variable AGN candidates, corresponding to active fractions of 0.17% ± 0.03% and 0.19% ± 0.02%, respectively. We found that spectroscopic approaches to AGN identification would have missed 81% of our ZTF IMBH candidates and 69% of our WISE IMBH candidates. Only nine candidates have been detected previously in radio, X-ray, and variability searches for dwarf galaxy AGN. The ZTF and WISE dwarf galaxy AGN with broad Balmer lines have virial masses of 10 5 M ⊙ < M BH < 10 7 M ⊙ , but for the rest of the sample, BH masses predicted from host galaxy mass range between 10 5.2 M ⊙ < M BH < 10 7.25 M ⊙ . We found that only 5 of 152 previously reported variability-selected AGN candidates from the Palomar Transient Factory in common with our parent sample were variable in ZTF. We also determined a nuclear supernova fraction of 0.05% ± 0.01% yr -1 for dwarf galaxies in ZTF. Our ZTF and WISE IMBH candidates show the promise of variability searches for the discovery of otherwise hidden low-mass AGN.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Comparing event generator predictions and ab-initio calculations of $\nu$-$^{12}$C neutral current quasi-elastic scattering at 1 GeV

The measurement of neutrino oscillations and exotic physics searches are important parts of the physics program in the near future, with new state-of-the-art experiments planned within the next decade. Future and modern experiments in these fields will make use of nuclear targets. Event Generators (EGs) are software used in the analysis of neutrino oscillation experiments. EGs use to predict kinematic observables for a range of neutrino energies. These simulations may lack physics captured by more rigorous theoretical calculations. This work compares EG performance to nuclear theory calculations by comparing observables generated in the two frameworks. We provide a common set of definitions between theory and experiment and assess the physics contained in EG simulations. Neutral current quasi-elastic (NCQE) scattering events for neutrinos and anti-neutrinos on a $^{12}$C target are simulated with a specific EG, NEUT, used by the T2K experiment for its analysis. The simulated cross sections are compared to analytic calculations from nuclear theory within the factorization scheme. We compare the NEUT implementation of two different models on nuclear spectral functions: the Relativistic Fermi Gas (RFG) and the correlated basis spectral function (CBF) to analytic calculations of the same models in the factorization scheme. For both nuclear physics models, we compare the appearance of features in the distributions relevant to experimental analyses. Qualitatively, the shape of the simulated distribution is similar to the one obtained through theory calculations; however, there are some discrepancies between the theory calculations and the NEUT simulation. While the EG simulations and analytic calculations with the same model of nuclear dynamics show similar overall features, there are still differences between the two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

OPF-Learn: An Open-Source Framework for Creating Representative AC Optimal Power Flow Datasets: Preprint

Increasing levels of renewable generation motivate a growing interest in data-driven approaches for AC optimal power flow (AC OPF) to manage uncertainty. However, a lack of disciplined dataset creation and benchmarking prohibits useful comparison between approaches in the literature. To instigate confidence, models must be able to reliably predict solutions across a wide range of operating conditions. This paper develops the OPF-Learn package for Julia and Python which uses a computationally efficient approach to create representative datasets that span a wide spectrum of the AC OPF feasible region. Load profiles are uniformly sampled from a convex set that contains the AC OPF feasible set. For each infeasible point found, the convex set is reduced using infeasibility certificates, found by utilizing properties of a relaxed formulation. The framework is shown to generate datasets which are more representative of the entire feasible space versus traditional techniques seen in the literature, improving machine learning model performance.

dataset↗
DOE OSTI2022

Integrated Operations for Nuclear Business Operation Model Analysis and Industry Validation

The purpose of this report is to refine and analyze five work reduction opportunities first presented in INL/EXT-21-64134, Process for Significant Nuclear Work Function Innovation Based on Integrated Operations Concepts. This report seeks to further refine and analyze five work reduction opportunities first presented in the original report. Researchers selected five work reduction opportunities from the full Integrated Operations for Nuclear (ION) suite. A selected group of utilities then verified details and inputs from the original report. Categories for verification included capital cost, technology requirements, and savings. Researchers then modeled the data points and data ranges using probabilistic analysis which predicts the likelihood of positive or negative net present value. Research results show four out of the five work reduction opportunities have a greater than fifty percent chance of a positive net present value outcome when analyzed independently. When the five work reduction opportunities are grouped and analyzed together the model indicates a sixty percent chance that the outcome of all five taken together will be positive. The nuclear industry should interpret these results as encouraging. In line with the ION model, positive financial analysis supports the investment of capital dollars into existing nuclear power plants along the ION model. Implementation of the five work reduction opportunities in this report is likely to result in substantive long-term savings for the owners and operators of domestic nuclear power plants.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2021

PERFORMANCE CHARACTERIZATION OF THE DIRECT CONTACT MEMBRANE DISTILLATION MODULE OPERATED WITH HIGHLY CONCENTRATED SOLUTION

The experimental study was conducted to characterize the performance of the flat sheet Direct Contact Membrane Distillation. The length degradation was studied in a short and long module with and without spacers. The experimental study is validated using the predicted flux for a wide range of operating conditions using deionized water. Three different membranes are used in the parametric study for feed Reynolds number varied between 500 and 2000, and inlet feed temperature varied between 45°C and 80°C. PTFE membrane was shown to be more effective than the PVDF due to its higher permeability coefficient and higher hydrophobicity. Fouling study was conducted on the selected PTFE membrane with various feed Reynolds numbers between 500 and 2000 and feed inlet temperature between 50°C and 80°C. Membranes used in the fouling study were characterized using scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) for the morphology and chemical composition of the fouling layer. 36 hours of operation with 10 wt% NaCl (100,000 ppm) at feed inlet temperatures 80°C and 60°C and fixed Reynolds 2000 demonstrated a drop in flux by 31% and 27%, respectively. Low flow rate and high temperature are favorable conditions for fouling formation and reduced permeate flux for highly concentrated solutions. The spacers improved the flux by 30.8% and 27.6% at the operating Reynolds numbers 2000 the short and long channel modules. This study helps to design and optimize DCMD modules for industrial-size desalination and water treatment applications.

Kim, Deliya↗
DOE OSTI2026

Case Study of Integrating High-Temperature Heat Pump with LiBr-H2O Absorption Chiller for Data Center Liquid Cooling

Data centers (DCs) are physical infrastructures that support artificial intelligence workloads. The rapid growth of artificial intelligence is putting substantial pressure on the US power grid. Most of electricity consumed by IT equipment, accounting for 50%-60% of total DC power, ultimately becomes waste heat. This heat is dissipated by DC’s cooling facilities, accounting for an additional 30%-40% of total DC power. Recovering and repurposing this waste heat offers a significant opportunity to enhance energy efficiency and reduce operating costs of DCs. One potential pathway is converting heat to cold using thermal-driven absorption chillers, therefore, reducing the power consumption in DC cooling facilities. Existing studies mainly demonstrate the technical and economic feasibility of repurposing DC’s waste heat for cooling applications but provide limited technical details on how to integrate the thermal-driven absorption chillers with DC cooling systems. In addition, the low-grade waste heat available from DCs must be upgraded to higher temperatures suitable for absorption chillers. This paper presents a case study on integrating high-temperature heat pumps with a LiBr-H2O absorption chiller to use DC waste heat for cooling. A thermodynamic model of single-effect, LiBr-H2O absorption chiller and an empirical model of high-temperature heat pumps were built. The case study considers ASHRAE W17 liquid-cooled DC, with facility service water supplied at 17.0℃ and returned at 25.3℃. The thermal behaviors of absorption chiller components were predicted for the generation temperature ranging from 75.0℃ to 115.0℃. Based on the available waste heat in the integrated system, two waste heat recovery strategies were evaluated: a facility service water-based strategy and cooling water-based strategy. Results indicated that the cooling water-based strategy achieves higher Coefficient of Performance (COPs) than the facility service water-based strategy. The relatively low cooling COPs of single-effect LiBr-H2O absorption chillers could be offset by high heating COP of high temperature heat pumps. The maximum cooling COP of absorption chiller and the overall COP of integrated systems occur at lower generation temperatures, but these conditions also yield lower cooling capacities. In practice, system operation should balance the trade-off between the COP and cooling capacity

Wang, Pengtao [ORNL] (ORCID:0000000214713429)↗
DOE OSTI2021

Correlating Time-Resolved Pressure Measurements With Rim Sealing Effectiveness for Real-Time Turbine Health Monitoring

Purge flow is bled from the upstream compressor and supplied to the under-platform region to prevent hot main gas path ingress that damages vulnerable under-platform hardware components. A majority of turbine rim seal research has sought to identify methods of improving sealing technologies and understanding the physical mechanisms that drive ingress. While these studies directly support the design and analysis of advanced rim seal geometries and purge flow systems, the studies are limited in their applicability to real-time monitoring required for condition-based operation and maintenance. As operational hours increase for in-service engines, this lack of rim seal performance feedback results in progressive degradation of sealing effectiveness, thereby leading to reduced hardware life. To address this need for rim seal performance monitoring, the present study utilizes measurements from a one-stage turbine research facility operating with true-scale engine hardware at engine-relevant conditions. Time-resolved pressure measurements collected from the rim seal region are regressed with sealing effectiveness through the use of common machine learning techniques to provide real-time feedback of sealing effectiveness. Two modelling approaches are presented that use a single sensor to predict sealing effectiveness accurately over a range of two turbine operating conditions. Results show that an initial purely data-driven model can be further improved using domain knowledge of relevant turbine operations, which yields sealing effectiveness predictions within three percent of measured values.

Compressors↗
DOE OSTI2021

Ruling Out the Onset of Color Transparency up to Q2 = 14.2 GeV2 in Quasielastic 12C(e,e'p) Scattering

Color Transparency (CT) is a prediction of QCD that at high momentum transfer Q2, a system of quarks which would normally interact strongly with nuclear matter could form a small color-neutral object whose compact transverse size would be maintained for some distance, passing through the nucleus undisturbed. A clear signature of CT would be a dramatic rise in nuclear transparency T with increasing Q2. CT emerges as a deviation from Glauber multiple scattering theory, which predicts constant T. While a rise in nuclear transparency would provide an unequivocal validation of QCD factorization theorems, the complex nature of nuclear interactions renders its observation difficult to predict. The E12-06-107 experiment at JLab measured T in quasielastic electron-proton scattering with carbon-12 and liquid hydrogen targets, for Q2 between 8.0 and 14.2 GeV2 , a range over which models of CT predicted that T might differ appreciably from Glauber calculations. Supported in part by US DOE grant DE-FG02-03ER41240.

Matter, John↗
DOE OSTI2022

A round-robin approach provides a detailed assessment of biomolecular small-angle scattering data reproducibility and yields consensus curves for benchmarking

Through an expansive international effort that involved data collection on 12 small-angle X-ray scattering (SAXS) and four small-angle neutron scattering (SANS) instruments, 171 SAXS and 76 SANS measurements for five proteins (ribonuclease A, lysozyme, xylanase, urate oxidase and xylose isomerase) were acquired. From these data, the solvent-subtracted protein scattering profiles were shown to be reproducible, with the caveat that an additive constant adjustment was required to account for small errors in solvent subtraction. Further, the major features of the obtained consensus SAXS data over the q measurement range 0–1 Å −1 are consistent with theoretical prediction. The inherently lower statistical precision for SANS limited the reliably measured q -range to <0.5 Å −1 , but within the limits of experimental uncertainties the major features of the consensus SANS data were also consistent with prediction for all five proteins measured in H 2 O and in D 2 O. Thus, a foundation set of consensus SAS profiles has been obtained for benchmarking scattering-profile prediction from atomic coordinates. Additionally, two sets of SAXS data measured at different facilities to q > 2.2 Å −1 showed good mutual agreement, affirming that this region has interpretable features for structural modelling. SAS measurements with inline size-exclusion chromatography (SEC) proved to be generally superior for eliminating sample heterogeneity, but with unavoidable sample dilution during column elution, while batch SAS data collected at higher concentrations and for longer times provided superior statistical precision. Careful merging of data measured using inline SEC and batch modes, or low- and high-concentration data from batch measurements, was successful in eliminating small amounts of aggregate or interparticle interference from the scattering while providing improved statistical precision overall for the benchmarking data set.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Leveraging hyperspectral phenotyping for accurate, non-destructive prediction of metabolite profiles in poplar under drought stress

Accurately predicting drought tolerance in woody perennial bioenergy crops is critical for sustainable biomass production under fluctuating precipitation. Hyperspectral imaging (HSI) in the visible-near-infrared (VNIR) and shortwave-infrared (SWIR) ranges offers a promising approach for predicting plant biochemical traits, yet its application in metabolite profiling remains underexplored. We integrated VNIR+SWIR HSI with untargeted metabolomics to investigate drought-induced metabolic shifts in Populus leaves from eight Populus genotypes. Metabolite profiling identified 127 compounds, with 73 showing significant drought responses spanning amino acids (AA), carbohydrates (CHO), phenolic glycosides (PG), organic acids (OA), fatty acids and alcohols (FA), terpenes (T), phenolic metabolites (P), and unclassified metabolites. Spectral analysis revealed consistently higher reflectance across VNIR and SWIR wavelengths in drought-stressed plants, corresponding with increased accumulation of AA and reduced CHO and PG levels. Least absolute shrinkage and selection operator (LASSO) regression modeling identified robust spectral predictors of metabolite concentrations, associating VNIR wavelengths (500–700 nm) predominantly with AA and P, whereas SWIR wavelengths (1680–1700 nm) reliably predicted CHO, OA, and T. Several stable spectral-metabolite associations persisted across the two watering regimes (drought vs. well-watered), highlighting their potential as spectral biomarkers for non-destructive stress monitoring. Minimal genotype-specific variation suggests that observed spectral and metabolic responses were driven primarily by environmental factors, likely reflecting limited genetic diversity among the commercial Populus genotypes examined. This work establishes VNIR+SWIR hyperspectral imaging as a powerful, non-destructive phenotyping tool for precision monitoring and targeted improvement of drought resilience in bioenergy crops.

Biochemical trait prediction↗
DOE OSTI2022

Correlating Time-Resolved Pressure Measurements With Rim Sealing Effectiveness for Real-Time Turbine Health Monitoring

Purge flow is bled from the upstream compressor and supplied to the under-platform region to prevent hot main gas path ingress that damages vulnerable under-platform hardware components. A majority of turbine rim seal research has sought to identify methods of improving sealing technologies and understanding the physical mechanisms that drive ingress. While these studies directly support the design and analysis of advanced rim seal geometries and purge flow systems, the studies are limited in their applicability to real-time monitoring required for condition-based operation and maintenance. As operational hours increase for in-service engines, this lack of rim seal performance feedback results in progressive degradation of sealing effectiveness, thereby leading to reduced hardware life. To address this need for rim seal performance monitoring, this study utilizes measurements from a one-stage turbine research facility operating with true-scale engine hardware at engine-relevant conditions. Time-resolved pressure measurements collected from the rim seal region are regressed with sealing effectiveness through the use of common machine learning techniques to provide real-time feedback of sealing effectiveness. Two modeling approaches are presented that use a single sensor to predict sealing effectiveness accurately over a range of two turbine operating conditions. Here, the results show that an initial purely data-driven model can be further improved using domain knowledge of relevant turbine operations, which yields sealing effectiveness predictions within 3% of measured values.

42 ENGINEERING↗
DOE OSTI2025

Intercomparison of Deep Learning Model Architectures for Atmospheric River Prediction

With a rapid surge in the application of machine learning (ML) for a diverse range of tasks in climate science, the present study addresses a challenge for climate scientists when selecting the optimal ML or deep learning (DL) architecture for a given application. In particular, a DL intercomparison study was performed with a focus on forecasting the position of atmospheric rivers (ARs) on short-range time scales (up to 5-day lead times). AR predictions from multiple DL architectures, including various types of convolutional autoencoders and a vision transformer (ViT), were compared against ECMWF ERA5 reanalysis and hindcasts from a global climate model. DL models with similar trainable parameters were trained on ERA5 reanalysis data and AR positions derived from a thresholding algorithm to ensure a fair comparison among the DL models. Each model’s performance and accuracy in forecasting AR location and key input fields within a 5-day window were assessed using metrics of root-mean-square error, anomaly correlation, and mean intersection over union. The ViT architecture outperformed other autoencoder models in most of the metrics. Incorporating additional meteorological fields only yielded slight improvements in forecasting certain fields at longer lead times. The results also suggest that a smaller number of input time steps or smaller number of autoregressive steps can achieve better prediction skills, while also improving the overall computational efficiency. This research offers valuable insights into the strengths and weaknesses of different DL techniques for AR forecasting, hopefully guiding the development of improved models for forecasting this phenomenon.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Quantifying Uncertainties in Earth's Energy Budget by Cloud Feedback and Ocean Heat Uptake Using E3SM-Slab Ocean Configurations

In order to improve predictive skills of Earth System Model, we need to better understand processes that control Earth's energy budget via ocean, atmosphere, and cryosphere interactions. Simulated energy budget in comprehensive Earth System Models shows a wide range, leading to large uncertainties in predicting Earth system dynamic and thermodynamic variations and associated social-economic impacts. Uncertainties in cloud feedbacks have been identified as the main cause of the large inter-model spread, but oceanic adjustments, especially those associated with ocean heat uptake (OHU) and the Atlantic Meridional Overturning Circulation (AMOC), also play an important role. In this proposed work, we focus on understanding the individual and combined roles of cloud feedbacks and ocean adjustments on modulating Earth's energy balance. This research is motivated by our overarching hypothesis that oceanic adjustment is a key source of uncertainty, in addition to those associated with the cloud feedbacks; further, the ocean adjustment and associated OHU work through the cloud feedbacks to modulate Earth's energy budget and temperature variations. We test this hypothesis using numerical experiments where we systematically enable and disable cloud feedbacks in conjunction with perturbations to OHU.

58 GEOSCIENCES↗
DOE OSTI2022

Snowmass2021 Cosmic Frontier Dark Matter Direct Detection to the Neutrino Fog

We present a summary of future prospects for direct detection of dark matter within the GeV/c2 to TeV/c2 mass range. This is paired with a new definition of the neutrino fog in order to better quantify the rate of diminishing returns on sensitivity due to irreducible neutrino backgrounds. A survey of dark matter candidates predicted to fall within this mass range demonstrates that fully testing multiple well-motivated theo-ries will require expanding the currently-funded generation of experiments down to and past the neutrino fog. We end with the status and plans for next-generation exper-iments and novel R&D concepts which will get us there.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Beirut Explosion Yield and Mushroom Cloud Height - Effects of the Source Environment

I use crater dimensions to estimate the yield of the August 4th, 2020 Beirut explosion to be equivalent to approximately 1.4 kilotons of TNT with a lower bound of about 0.7 kilotons. Based on the amount of ammonium nitrate reported to have been stored at the Beirut harbor, I assume an upper bound for the yield of 2.75 kilotons. However, it is highly likely that the yield was less than 2.75 kilotons, since reported values for TNT equivalence of ammonium nitrate are typically much less than one hundred percent. The crater-size based yield estimates are based on crater radius estimates from satellite imagery and empirical curves and data for scaled crater radius from past chemical and nuclear explosions. I present evidence that suggests that the relatively large crater radius is due to a high degree of coupling of shock wave energy to the surrounding medium and a reduction of the effective stress because of a high level of saturation of the geologic media beneath the explosion. I provide yield estimates based on seismic body-wave magnitude and crater depth as corroborating evidence. I compare preliminary estimates for the maximum debris cloud height, based on cell phone videos/images, with predicted maximum heights for this yield range from empirical formulas and numerical cloud-rise models. Based on a preliminary analysis of cell phone footage, the observed maximum cloud height appears to be approximately 1600 m. This is much lower than that predicted using standard empirical formulas and buoyant cloud rise models. I present results from a modified buoyant cloud rise model that more accurately predicts the maximum cloud height by allowing for the inclusion of a fixed amount of air and/or water into the fireball at the start of cloud rise. The amount of mass that needs to be added at the start, to reproduce the observed maximum cloud height, is relatively small compared to the total mass entrained during cloud rise. A much greater amount of dry air or debris is required, relative to water, for an equivalent reduction in maximum cloud height. The ammonium nitrate is one possible source for water in the fireball since it was being stored in a very humid environment and ammonium nitrate is known to be hygroscopic. The ground beneath the explosion, especially if it were saturated, and the nearby harbor could also have been sources for water or debris in the fireball.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗