Search NASASearch

SEARCH · Search NASA

Results for “rule of mixtures”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

3,213 records · Page 89

Integration and Optimization of Loads, and Renewables for Grid-Interactive Efficient Buildings

Deploying advanced building control strategies in small- and medium-sized commercial buildings (SMBs) is critical but constrained by two major challenges: (1) the lack of sensor and control infrastructure (SCI) and (2) the significant engineering effort required for implementation and configuration. While these barriers limit large-scale adoption in SMBs, they remain underexplored in the literature, which has largely emphasized feasibility over scalability.

25 ENERGY STORAGE

Large language model-driven database for thermoelectric materials

Thermoelectric materials have the ability to convert waste heat into electricity, offering a valuable solution for energy harvesting. However, their widespread use is hindered by low conversion efficiency, the reliance on expensive rare earth elements, and the environmental and regulatory concerns associated with lead-based materials. A fast and cost-effective way to identify highly efficient thermoelectric materials is through data-driven methods. These approaches rely on robust and comprehensive datasets to train models. Although there are several databases on thermoelectric materials, there is still a need to collect and integrate experimental data from peer-reviewed research articles to capture diverse compositions and properties of materials. Here, in this work, we developed a comprehensive database of 7,123 thermoelectric compounds, containing key information such as chemical composition, structural detail, seebeck coefficient, electrical and thermal conductivity, power factor, and figure of merit (ZT). We used the GPTArticleExtractor workflow, powered by large language models (LLM), to extract and curate data automatically from the scientific literature published in Elsevier journals. This process enabled the creation of a structured database that addresses the challenges of manual data collection. The open access database could stimulate data-driven research and advance thermoelectric material analysis and discovery.

Database

A Review of Superconducting Electric Machines with On-Board Cryocoolers

This paper reviews the evolution and emerging direction of superconducting electric machines that employ onboard cryocoolers integrated directly into the rotor, eliminating the need for cryogenic fluid coupling and, in some cases, rotary seals. Traditional low-temperature superconducting (LTS) machines relied on external cryogenic systems and liquid helium transfer couplers, which introduced excessive complexity, poor reliability, and significant parasitic energy losses. The advent of high-temperature superconductors (HTS) has enabled compact, closed-cycle cryocoolers that support self-contained, fluid-free refrigeration architectures suitable for rotating applications. This paper examines the key technological challenges associated with on-board cryocooler integration and reviews three representative efforts by KAIST, NASA, and Hinetics, each illustrating distinct strategies and milestones toward practical implementation. KAIST demonstrated early proof-of-concept for rotating machines with on-board cryocoolers, NASA developed a shaft-integrated Stirling-type pulse tube cryocooler for a 1.4 MW hybrid-electric motor, and Hinetics achieved full-scale validation of a self-contained HTS rotor incorporating a commercial Stirling cryocooler and spoke-suspension torque tube. Collectively, these achievements confirm the technical feasibility of on-board cryogenic refrigeration and highlight steady progress toward compact and efficient superconducting rotating systems across various applications. Embedding cryocoolers directly within the rotor enables practical, efficient, and commercially viable superconducting propulsion technologies.

Cryogenics

Dynamic Analysis of Reynolds Number Effects on Trailing Edge Transonic Vortex Shedding and Its Impact on Turbine Blade Aerodynamic Performance

In this work, we will discuss observations from images acquired from a time-resolved, high-speed self-aligned focusing Schlieren campaign that was performed at the CW-22 facility at NASA Glenn Research Center to understand the dynamic behavior of thick trailing-edge high-pressure turbine blades simulating a ceramic matrix composite (CMC) construction at high inlet turbulence conditions. For the CMC-9 blade, which has a trailing edge thickness of 9% of the axial chord, we identified a regime where an excessive total pressure loss (loss anomaly) is observed only for a narrow range of Reynolds numbers at a fixed exit Mach number of 0.74. The loss anomaly is qualitatively explained by our images, which were taken at 10 distinct blade Reynolds numbers spanning a factor of 6. The images show a significant increase in energy related to the oscillations due to transonic vortex shedding at the Reynolds numbers related to the high loss conditions. This increased energy leads to the formation of strong acoustic waves that turn into shock waves at the highest loss conditions. From our observations stemming from Spectral POD analysis of the high-speed images, we see the acoustic waves produced by the trailing edge vortex shedding exist in all conditions tested; but the shedding frequency has a very slight trend upwards as the Reynolds number is increased, varying about 6% in the range tested. Considering this variation of shedding frequency as a function of Reynolds number, which is well-established for other bluff-body flows, we stipulate there may be a potential feedback mechanism involving an acoustic information transfer path across neighboring blades that may explain why only a narrow range of Reynolds numbers displays strong, shock-forming vortex shedding. We consider a few feedback paths and examine the timing based on the mean flow field from a high-resolution LES simulation. It appears that all feedback mechanisms are viable, presenting an integer number of delay cycles with respect to disturbances generated at the trailing edge. Most noteworthy, however, is the acoustic/shock-boundary layer interaction mechanism at the blade geometric throat. Based on our analysis, this mechanism likely plays an important role in realistic, curved turbine blade passages.

Aerodynamics

Improving Marine Energy Production Through Commercialization of a Low Cost, Drag-Reducing Slippery Coating (CRADA 679 Abstract)

Marine energy capture systems offer great promise for providing clean energy, but they operate in a challenging and dynamic environment and must be optimized to the highest extent possible. Computational studies predict that drag reduction on marine energy and blue economy systems will result in meaningful improvements in energy efficiency. Based on extensive coating experience, PNNL is proposing to bring to market a new drag-reducing coating called Superhydrophobic Lubricant-Infused Drag-Efficient Coating – SLIDE-Coat. PNNL has a deep knowledge base regarding this class of slippery coatings, and we have a group of enthusiastic industry partners who have committed to partnering, conducting field testing, and providing well over 50% cost share. In addition to validating the technology, the team will create a commercialization roadmap to ensure the commercial success of the technology after the government-sponsored two-year program is complete. The main technical goal is to design, manufacture, and experimentally validate a new coating that can reduce hydrodynamic skin friction drag by 20%. The main commercialization goal is to develop a roadmap that identifies activities needed to complete SLIDE-Coat’s development after the conclusion of this project. Year 1 will focus on adaptation and modification of the existing SLIC coating system to optimize drag reduction and assessment and quantification of drag reduction on relevant materials in a laboratory setting. Year 2 will focus on optimizing and demonstrating drag reduction with preferred coatings. The manufacturability, ease of application, adhesion to relevant surfaces, and consistency will be assessed. Quantification of drag reduction on prototype materials in a relevant marine field setting will be executed.

16 TIDAL AND WAVE POWER

Electrodynamic Tethers. 1: Power Generator in LEO. 2: Thrust for Propulsion and Power Storage

An electrodynamic tether consists of a long insulated wire in space whose orbital motion cuts across lines of magnetic flux to produce an induce voltage that in typical low orbits averages about 200 v/km. Such a system should be capable of generating substantial electrical power, at the expense of IXB drag acting on its orbital energy. If a reverse current is driven against the induced voltage, the system should act as a motor producing IXB thrust. A reference system was designed, capable of generating 20 KW of power into an electrical load located anywhere along the wire at the expense of 2.6N (20,000 J/sec) drag on the wire. In an ideal system, the conversion between mechanical and electrical energy would reach 100% efficiency. In the actual system part of the 20 KW is lost to internal resistance of the wire, plasma and ionosphere, while the drag force is increased by residual air drag. The 20 KW PMG system as designed is estimated to provide 18.7 KW net power to the load at total drag loss of 20.4 KJ/sec, or an overall efficiency of 92%. Similar systems using heavier wire appear capable of producing power levels in excess of 1 Megawatt at voltages of 2-4 KV, with conversion efficiency between mechanical and electrical power better than 95%. The hollow cathode based system should be readily reversible from generator to motor operation by driving a reverse current using onboard power.

James E Mccoy

Correlating Impacts of Injected Fuels on Carbon Emissions in Blast Furnace with Computational Fluid Dynamics Modeling

A major challenge for steelmaking is the reduction of CO 2 emissions. In this regard, the blast furnace (BF) is critical due to the high associated CO 2 levels. This investigation assesses the impact of tuyere‐injected fuels on BF CO 2 emissions. Specifically, computational fluid dynamics results obtained previously at Purdue University Northwest are analyzed to obtain CO 2 emissions when natural gas (NG), syngas, hydrogen, or hydrogen/NG are injected. CO 2 emissions are compared with those produced when 95 kg of NG/thm is injected. Among these scenarios, the largest CO 2 reduction occurs when 102 kg of syngas/thm (COG feedstock #1) is injected at 973 K, reducing CO 2 by 190.6 kg thm −1 . The largest CO 2 reduction obtained with NG occurs when 130 kg thm −1 is injected at 600 K, reducing emissions by 65 kg thm −1 . H 2 injection also reduces CO 2 , but requires careful adjusting to reach stable operation. For instance, injecting 35 kg of H 2 /thm reduces CO 2 by 52 kg thm −1 . Increasing gaseous injection rates can significantly reduce CO 2 emissions, with fuel preheating providing an addendum, but high injection rates can lead to unstable operation. Furthermore, results show a correlation between CO 2 emissions and average temperature of shaft region for multiple fuels and injection conditions.

Metallurgy & Metallurgical Engineering

Numerical simulation of frost formation and heat transfer on fin-and-tube heat exchangers in turbulent cross-flow

Frost formation in fin-and-tube heat exchangers in turbulent cross-flow presents significant challenges in industrial refrigeration applications, affecting heat transfer efficiency and operational reliability. The purpose of this work is to investigate frost deposition and growth on a staggered bank of a fin-and-tube freezer coil under turbulent forced convection conditions. The focus here is on investigating conditions that closely replicate real-world scenarios in large walk-in industrial freezers. Using a direct numerical simulation approach, we examine the flow dynamics and thermal behaviour in the presence of frost, considering turbulent regimes characterized by a Reynolds number in the range 1050 ≤ R e D , avg ≤ 4800 , with the characteristic length being the outer diameter of the tube and the velocity being the bulk fluid velocity between the plates (fins). Computational fluid dynamics simulations are employed to resolve the interactions between turbulent airflow and the frost layer. Our approach incorporates a modified immersed boundary method and a slow-time acceleration technique to address the complex dynamic interface between the continuously evolving frost layer and the flowing air stream. Our findings indicate that frost forms more on the sides of the finned surfaces (plates) and less on the tubes themselves. This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.

Science & Technology - Other Topics

Prototype Demonstration of Solar Carbothermal System to Extract Oxygen from Regolith

The Carbothermal Reduction Demonstration (CaRD) project was an effort to develop a prototype system to demonstrate the extraction of oxygen from simulated lunar regolith using concentrated solar energy and a carbothermal reaction. The prototype consisted of a deployable solar concentrator capable of tracking the sun, carbothermal reactor, fluid system, gas analysis, and a solar concentrator control system consisting of avionics and software. These subsystems were developed by multiple NASA centers and a private industry partner, Sierra Space. The various teams worked together to define requirements and interfaces to successfully assemble the complex system and demonstrate an integrated solar carbothermal process. The solar concentrator developed at Glenn Research Center (GRC) was designed to be stowed for a launch environment then deployed on the lunar surface. It utilized a crossed dragone configuration of composite mirrors to direct horizontal sunlight onto a target 90° from the incoming sunlight. The key performance parameters for the solar concentrator were efficiency and power density. The carbothermal reactor was developed by Sierra Space through a separate project called the Carbothermal Oxygen Production Reactor (COPR) where it successfully demonstrated a fully automated process in a thermal vacuum environment. The fluid system needed for the carbothermal reaction was also developed by Sierra Space and successfully demonstrated in the same thermal vacuum test. The gas analysis system was developed at Kennedy Space Center (KSC) and was required to determine the amount of oxygen extracted during each test. The gas analysis system was based on the Mass Spectrometer Observing Lunar Operations (MSOLO) instrument. Avionics and software for the CaRD prototype were also developed at KSC and based on experience with MSOLO avionics and software. The control system was designed to stow, deploy, track the sun, and perform beam alignment of the concentrated light. The prototype subsystems were integrated and tested at Johnson Space Center’s (JSC) Energy Systems Test Area. A heliostat was used to direct sunlight toward the prototype in a way that is representative of the sunlight conditions at the south pole of the Moon. When concentrated sunlight was focused on simulated lunar regolith within the reactor, the gas analysis team confirmed the presence of carbon monoxide gas, which confirmed that a solar carbothermal reaction took place. The key performance parameter for the integrated prototype was grams of oxygen extracted per kilowatt hour of energy arriving at the concentrator primary mirror. The prototype design successfully demonstrated end-to-end capability and further steps to achieve a flight capable system have been defined. With lunar data, engineers would be able to design a scaled-up system capable of extracting oxygen from regolith at useful quantities for crew life support and rocket propellant. On the long term, this method of In-Situ Resource Utilization could be used to drastically reduce the cost and risk of a sustained human presence on the Moon by reducing the amount of oxygen that would have to be delivered.

Aaron Paz

AC and DC Fault Management for Megawatt Electrified Aircraft Electrical Powertrains Task 3: Lifetime and Reliability of Electrical Insulators

This research project was a collaborative investigation between researchers at the RTX Technology Research Center (RTRC) and the University of Texas at Austin and made a significant contribution to enabling electric aircraft. The transport of electric power between the points of generation and use requires power cables. These cables must be smaller, lighter and provide a more predictable life than power cables used in stationary applications. Consequently, this investigation provided heretofore unavailable information supporting the safety and reliability of smaller lighter power cables for electrified aircraft. In addition, the research identified key additional engineering data needed to support quantitative reliability assessments. Important advances included: • Demonstrated that at least one manufacturer can make a novel, smaller, lighter power cable that is free from serious defects. • Developed and published an appropriate analytical construct to describe the life of this novel cable. This is a necessary step for use in aviation where the understanding of remaining life is critical. • Demonstrated thermal-mechanical aging that suggested 1000+ flights before the thermal-mechanical processes produced defects large enough that the defect growth was accelerated electrically. • Showed that electrical aging took place at two rates. The first possibly lasting weeks to months and the second possibly days to weeks. If robust, this provides a good diagnostic for cable replacement. • Demonstrated that the traditional electrical testing of cable materials using manufactured voids can be misleading due to the size of the voids. Emerging laser drilling technology permitted demonstration that the physics of failure in realistically small voids is different from that in the unrealistically large voids used in earlier research, which is very important for high-quality, high-performance, small aircraft cables. Although this project represents a significant contribution to the specifics of cable aging in the aircraft environment, important additional research remains to be completed, including: • Non-uniform thermal cycling by applying the heat from the center conductor to maximize thermal stress next to the core area where the electric gradient is the strongest. This builds on the uniform thermal cycling that has been completed. • The augmentation of the thermal-mechanical failure rate by electrical processes. Better understanding of these time constants strongly affects the ability to predict life. • Termination design: Terminations provide not only electrical reflection potential, but a location for a series arc fault and an area where ozone can diffuse into the center conductor and negatively affect cable insulation. • The abrasion and ozone resistance of the cable jacket. • Pressure cycling as an accelerant of thermal, mechanical, and/or electrical aging. • Possible methods for online PD detection and offline PD localization

model

A high reliability battery management system

Over a period of some 5 years Canadian Astronautics Limited (CAL) has developed a system to autonomously manage, and thus prolong the life of, secondary storage batteries. During the development, the system was aimed at the space vehicle application using nickel cadmium batteries, but is expected to be able to enhance the life and performance of any rechargeable electrochemical couple. The system handles the cells of a battery individually and thus avoids the problems of over, and under, drive that inevitably occur in a battery of cells managed by an averaging system. This individual handling also allow cells to be totally bypassed in the event of failure, thus avoiding the losses associated with low capacity, partial short circuit, and the catastrophe of open circuit. The system has an optional capability of managing redundant batteries simultaneously, adding the advantage of on line reconditioning of one battery, while the other maintains the energy storage capability of the overall system. As developed, the system contains a dedicated, redundant, microprocessor, but the capability exists to have this computing capability time shared, or remote, and operating through a data link. As adjuncts to the basic management system CAL has developed high efficiency, polyphase, power regulators for charge and discharge power conditioning.

Moody, M. H.

Evaluation of AMSOIL® -ANT PGW Coolant Formula Change and Super Space AMSOIL Development

AMSOIL ® Propylene Glycol Water (PGW), is the baselined internal thermal control fluid for multiple manned spacecraft including Gateway (HALO, IHAB, and ALM modules) and Orion. The use of AMSOIL-ANT PGW was originally validated through extensive NASA/Collins materials-compatibility testing (circa 2008–2015). However, in late 2019, AMSOIL implemented an unannounced change in its PG inhibitor package. Because of this reformulation, concerns around materials compatibility arose. Therefore, NASA initiated corrosion rate and coolant stability testing in 2024. Results showed that the reformulated AMSOIL PG produced substantially elevated corrosion rates in aluminum alloys (about two times when compared to the original AMSOIL PG formula) accompanied by visible surface degradation. Coolant stability testing indicated accelerated propylene-glycol breakdown as well, with glycolate levels about nine times higher than the original formulation. Based on these findings, NASA Materials & Processes and Thermal Control Systems groups have baselined the use of the original PGW chemistry for all spacecraft use. In response, AMSOIL produced a reformulated variant, “Super Space AMSOIL” (ANT-SSA), compliant with MPCV 70156.This paper documents the reformulation testing completed, details on the formulation change, and the development of Super Space AMSOIL.

Woody Beringer

A Study of Space Environment Effect on Highly Thermally Conductive Hybrid Carbon Fiber Polymer Composites

A set of novel highly thermally conductive hybrid carbon fiber (CF) polymer composites has been developed for lightweight thermal radiator applications in space missions. This study investigates the effects of the space environment on these materials following exposure in low-Earth orbit (LEO) during the Materials International Space Station Experiment (MISSE)-17 flight mission, where samples experienced 159 days of combined atomic oxygen (AO), ultraviolet (UV) radiation, high vacuum, space radiation and thermal cycling. Post-flight characterization included weight loss, surface morphology, thermo-optical properties, molecular structures, glass transition temperature, thermal degradation and thermal conductivity analyses. The pyrolytic graphite sheet (PGS) samples exhibited negligible weight loss, stable thermo-optical property, and only minor oxidation signature on the exposed surface. Although AO erosion of the epoxy polymer matrix was evident, carbon nanotube (CNT)-infused PGS/CF epoxy composites retained high thermal emissivity and preserved their high thermal conductivities. These results demonstrate that the novel highly thermally conductive hybrid CF composites possess strong environmental resilience and are promising candidates for lightweight thermal radiators and thermal management components in future space exploration missions.

Space Environment

Evaluation of AMSOIL ® -ANT PGW Coolant Formula Change and Super Space AMSOIL ® Development

AMSOIL ® Propylene Glycol Water (PGW), is the baselined internal thermal control fluid for multiple manned spacecraft including Gateway (HALO, IHAB, and ALM modules) and Orion. The use of AMSOIL-ANT PGW was originally validated through extensive NASA/Collins materials-compatibility testing (circa 2008–2015). However, in late 2019, AMSOIL implemented an unannounced change in its PG inhibitor package. Because of this reformulation, concerns around materials compatibility arose. Therefore, NASA initiated corrosion rate and coolant stability testing in 2024. Results showed that the reformulated AMSOIL PG produced substantially elevated corrosion rates in aluminum alloys (about two times when compared to the original AMSOIL PG formula) accompanied by visible surface degradation. Coolant stability testing indicated accelerated propylene-glycol breakdown as well, with glycolate levels about nine times higher than the original formulation. Based on these findings, NASA Materials & Processes and Thermal Control Systems groups have baselined the use of the original PGW chemistry for all spacecraft use. In response, AMSOIL produced a reformulated variant, “Super Space AMSOIL” (ANT-SSA), compliant with MPCV 70156.This paper documents the reformulation testing completed, details on the formulation change, and the development of Super Space AMSOIL.

David Brockett

Atomistic Simulation of Glasses and Amorphous Materials: Challenges and Opportunities for the Next Decade

Atomistic simulations have become indispensable tools for understanding glass structure, dynamics, and properties, yet persistent challenges limit their predictive power. This perspective examines three interconnected issues, namely glass formation procedures, interatomic potential development, and machine learning applications, which emerged from the 5th International Workshop on Challenges of Atomistic Simulations of Glasses and Amorphous Materials. We identify convergent community priorities for (i) standardized validation protocols, (ii) curated benchmark datasets with complete metadata, and (iii) open repositories for glasses. A systematic was forward is provided by a hierarchical validation framework for assessing the structural fidelity, property prediction, and behavioral realism of simulation techniques. Looking ahead, transformative advances are promised by the fusion of classical techniques with machine learning based approaches, for instance, by integrating swap Monte Carlo with machine-learning (ML) potentials, leveraging foundation models through transfer learning, and finetuning ML potentials with experimental data. Progress depends on the community committing to validated models, reproducible protocols, and sustained data sharing.

Krishnan, N. M. Anoop

Effect of Fe on Co-Based SiO2Al2O3 Mixed Support Catalyst for Fischer–Tropsch Synthesis in 3D-Printed SS Microchannel Microreactor

This research explores the effect of a composite support of SiO2 and Al2O3 with Fe and Co incorporated as catalysts for Fischer–Tropsch synthesis (FTS) using a 3D-printed stainless steel (SS) microchannel microreactor. Two mesoporous catalysts, FeCo/SiO2Al2O3 and Co/SiO2Al2O3, were synthesized via a one-pot (OP) method and extensively characterized using N2 physisorption, XRD, SEM, TEM, H2-TPR, TGA-DSC, FTIR, and XPS. H2-TPR results revealed that the synthesis method significantly affected the reducibility of metal oxides, thereby influencing the formation of active FTS sites. SEM-EDS and TEM further revealed a well-defined hexagonal matrix with a porous surface morphology and uniform metal ion distribution. FTS reactions, carried out in the 200–350 °C temperature range at 20 bar with a H2/CO molar ratio of 2:1, exhibited the highest activity for FeCo/SiO2Al2O3, with up to 80% CO conversion. Long-term stability was evaluated by monitoring the catalyst performance for 30 h on stream at 320 °C under identical reaction conditions. The catalyst was initially active for the methanation reaction for up to 15 h, after which the selectivity for CH4 declined. Correspondingly, the C4+ selectivity increased after 15 h of time-on-stream, indicating a shift in the product distribution toward longer-chain hydrocarbons. This trend suggests that the catalyst undergoes gradual activation or restructuring under reaction conditions, which enhances chain growth over time. The increase in C4+ products may be attributed to the stabilization of the active sites and suppression of methane or light hydrocarbon formation.

Biochemistry & Molecular Biology

Block-Type Antiferromagnetism in Single Chain Quasi-One-Dimensional K 3 ⁢Fe 2 ⁢Se 4

One-dimensional (1D) structures provide a unique platform to study the correlated quantum interactions and phase transitions such as unconventional magnetism and superconducting states. Here, we report that iron chalcogenide K 3 ⁢Fe 2 ⁢Se 4 exhibits an unusual block-type canted antiferromagnetic (AFM) order with a clear single chain quasi-1D structure, which is structurally different from the two-leg ladder BaFe 2 ⁢Se 3 , through both experimental measurements and density matrix renormalization group (DMRG) calculations. The narrow bandgap semiconductor K 3 ⁢Fe 2 ⁢Se 4 has a quasi-1D edge-shared FeSe4 tetrahedra chain structure and orders antiferromagnetically below 110 K. The magnetic moments couple antiferromagnetically along the quasi-1D chain direction of the 𝑏 axis and form an up-down-down-up (↑−↓−↓−↑)–like spin structure with a commensurate propagation vector 𝒌=⁢(0,0,0), where block-type spin ↑−↑ or ↓−↓ coupling are between the longer Fe-Fe bonds of the quasi-1D chain. DMRG results show that block antiferromagnetic state is stable in K 3 ⁢Fe 2 ⁢Se 4 and reveal that the block-ordered arrangement of Fe 2.5+ ions spins arise from the competition between ferromagnetic and AFM interaction in the presence of strong electronic correlation. Our research results not only report the discovery of a clear block-type canted antiferromagnetic structure in a real quasi-1D chain material but also provide a theoretical approach to understand the block-type antiferromagnetism in quasi-1D iron chalcogenides.

antiferromagnetism

Machine learning approach for vibronically renormalized electronic band structures

Here, we present a machine learning (ML) method for efficient computation of vibrational thermal expectation values of physical properties from first principles. Our approach is based on the nonperturbative frozen phonon formulation in which stochastic Monte Carlo algorithm is employed to sample configurations of nuclei in a supercell at finite temperatures based on a first-principles phonon model. A deep-learning neural network is trained to accurately predict physical properties associated with sampled phonon configurations, thus bypassing the time-consuming ab initio calculations. To incorporate the point-group symmetry of the electronic system into the ML model, group-theoretical methods are used to develop a symmetry-invariant descriptor for phonon configurations in the supercell. We apply our ML approach to compute the temperature dependent electronic energy gap of silicon based on density functional theory (DFT). We show that, with less than a hundred DFT calculations for training the neural network model, an order of magnitude larger number of sampling can be achieved for the computation of the vibrational thermal expectation values. Our work highlights the promising potential of ML techniques for finite temperature first-principles electronic structure methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND