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963 records · Page 42

Spacecraft Radiator Protection from Ionizing Radiation, Dust, and Excessive Heat Loss

Under a Phase II SBIR project funded by NASA Johnson Space Center (Contract No. 80NSSC25C0088), Analytical Scientific Products LLC (ASP) has been developing an actively controlled louver to protect spacecraft radiators from degradation due to exposure to various types of environmental conditions. Of particular interest are ionizing radiation during spacecraft transit through the Van Allen belts, dust during spacecraft landing and surface operations on the moon, and excessive heat loss during the long lunar night especially near the poles where the local ambient temperatures can drop below -200°C. Exposure to ionizing radiation and dust can degrade the optical properties of the radiator coating that in turn reduces its ability to reject excess heat from the spacecraft into the environment. Exposure to the extremely low temperature conditions during the lunar night near the poles can freeze the radiator fluids that can compromise the integrity of the radiator. Passive louvers constructed using thick aluminum vanes are used currently to protect spacecraft radiators from some of the above effects, but they have several drawbacks: (i) their high aerial density makes it impractical to scale them to protect the much larger spacecraft radiators needed for future manned missions to the moon and beyond, (ii) the bimetallic actuators used to open and close the vanes in passive louvers rely on external temperature alone and so the louver cannot offer protection from dust and ionizing radiation when the ambient temperatures are high, and (iii) the bimetallic actuators need time scales of the order of hours to open and close. We have addressed the above limitations of passive louvers through the development of a low aerial density and rapidly actuating actively controlled louver. It is constructed from a custom alloy that offers much higher levels of protection against the ionizing radiation, dust and excessive heat loss at a fraction of weight compared to passive louvers while providing opening and closing time scales of the order of a second. Our modular design makes it easy to scale the system up or down depending on the application. We have recently constructed a 31 inch × 31 inch module of this louver and tested its functionality and effectiveness. These tests have shown that the louver can be opened and closed in less than 2 s. It reduces the transmission of ionizing radiation by 78% to 100% (depending on the radiation source), dust transmission by more than 93%, and heat loss by more than 97%. We are currently preparing to evaluate this device at the Johnson Space Center’s cryogenic vacuum chamber where it can be subjected to simulated lunar surface conditions. This paper provides a detailed discussion of the test designs as well as the data from tests that demonstrate the effectiveness in reducing the transmission of ionizing radiation, dust, and heat under laboratory conditions.

Radiator

Spacecraft Radiator Protection from Ionizing Radiation, Dust, and Excessive Heat Loss

Under a Phase II SBIR project funded by NASA Johnson Space Center (Contract No. 80NSSC25C0088), Analytical Scientific Products LLC (ASP) has been developing an actively controlled louver to protect spacecraft radiators from degradation due to exposure to various types of environmental conditions. Of particular interest are ionizing radiation during spacecraft transit through the Van Allen belts, dust during spacecraft landing and surface operations on the moon, and excessive heat loss during the long lunar night especially near the poles where the local ambient temperatures can drop below -200°C. Exposure to ionizing radiation and dust can degrade the optical properties of the radiator coating that in turn reduces its ability to reject excess heat from the spacecraft into the environment. Exposure to the extremely low temperature conditions during the lunar night near the poles can freeze the radiator fluids that can compromise the integrity of the radiator. Passive louvers constructed using thick aluminum vanes are used currently to protect spacecraft radiators from some of the above effects, but they have several drawbacks: (i) their high aerial density makes it impractical to scale them to protect the much larger spacecraft radiators needed for future manned missions to the moon and beyond, (ii) the bimetallic actuators used to open and close the vanes in passive louvers rely on external temperature alone and so the louver cannot offer protection from dust and ionizing radiation when the ambient temperatures are high, and (iii) the bimetallic actuators need time scales of the order of hours to open and close. We have addressed the above limitations of passive louvers through the development of a low aerial density and rapidly actuating actively controlled louver. It is constructed from a custom alloy that offers much higher levels of protection against the ionizing radiation, dust and excessive heat loss at a fraction of weight compared to passive louvers while providing opening and closing time scales of the order of a second. Our modular design makes it easy to scale the system up or down depending on the application. We have recently constructed a 31 inch × 31 inch module of this louver and tested its functionality and effectiveness. These tests have shown that the louver can be opened and closed in less than 2 s. It reduces the transmission of ionizing radiation by 78% to 100% (depending on the radiation source), dust transmission by more than 93%, and heat loss by more than 97%. We are currently preparing to evaluate this device at the Johnson Space Center’s cryogenic vacuum chamber where it can be subjected to simulated lunar surface conditions. This paper provides a detailed discussion of the test designs as well as the data from tests that demonstrate the effectiveness in reducing the transmission of ionizing radiation, dust, and heat under laboratory conditions.

Radiator

International Space Station Lithium-Ion Battery

The International Space Station (ISS) primary Electric Power System (EPS) currently uses Nickel-Hydrogen (Ni-H2) batteries to store electrical energy. The electricity for the space station is generated by its solar arrays, which charge batteries during insolation for subsequent discharge during eclipse. The Ni-H2 batteries are designed to operate at a 35 depth of discharge (DOD) maximum during normal operation in a Low Earth Orbit. Since the oldest of the 48 Ni-H2 battery Orbital Replacement Units (ORUs) has been cycling since September 2006, these batteries are now approaching their end of useful life. In 2010, the ISS Program began the development of Lithium-Ion (Li-Ion) batteries to replace the Ni-H2 batteries and concurrently funded a Li-Ion ORU and cell life testing project. When deployed, they will be the largest Li-Ion batteries ever utilized for a human-rated spacecraft. This paper will include an overview of the ISS Li-Ion battery system architecture, the Li-Ion battery design and development, controls to limit potential hazards from the batteries, and the status of the Li-Ion cell and ORU life cycle testing.

battery

A Study of the Aligned-Grid Retarding Potential Analyzer for Electric Propulsion Applications

During the development of energy analyzers for NASA’s Solar Electric Propulsion Plasma Diagnostics Package, detailed studies were performed to compare the benefits and drawbacks of different types of gridded potential analyzers. In particular, modeling and testing were performed on three types of retarding potential analyzer with aligned grids, and one type with unaligned grids. Additionally, a type of gridded energy analyzer was tested. Analyses of the model and test results showed that manufacturing an analyzer with aligned grids required greater precision and knowledge than other analyzers. A properly designed analyzer with aligned grids exhibited superior signal level, acceptance angle control, energy resolution, and compactness compared to an analyzer with unaligned grids. Additionally, the gridded energy analyzer was found to accept a broad range of incidence angles while having superior signal, energy resolution, and compactness compared to retarding potential analyzer with unaligned grid. This article describes the basic design principles deployed in the study, the associated modeling work, and the characterization tests that were performed. The article summarizes the benefits and drawbacks associated with each type of energy analyzer tested.

Electric Propulsion

Design and Optimization of an Open Rotor Stage

Open rotor propulsors enable greatly increased effective bypass ratios over current aircraft engines, resulting in significantly improved efficiencies. One of the most promising of these geometries is the “open fan”, which consists of a single rotor followed by a single stator. This configuration will be referred to as an “open rotor stage” for design work at NASA. In this work we consider the multidisciplinary design and optimization of an open rotor stage using a variety of 2D and 3D techniques. The 2D aerodynamic techniques used for design include a 2D Trefftz plane method, axisymmetric throughflow, and quasi-3D blade-to-blade CFD. Aerodynamic performance is prioritized, while structural requirements are met and some acoustic considerations are included. Between the rotor, stator, and hub profiles, a total of 101 design variables are used. Differences in the process of designing an open rotor stage vs. designing other high-speed propellers are also discussed. The current design, the NASA Optimized Propulsor for Efficiency and Noise (N-OPEN-1), achieves 84.7% net efficiency as predicted by 3D CFD, with further improvements expected to be possible. This design makes effective use of a slower rotor and a less tip-loaded work distribution than typical single-rotation propellers, allowing the stator to produce 14.8% of the thrust. Laminar flow on the blades was responsible for a 1.7% efficiency benefit and warrants further study.

Open rotors

Crack‐Free Single‐Crystalline LiNiO 2 for High Energy Density All‐Solid‐State Batteries

Abstract Single‐crystalline layered oxide (LiNi 1‐ x ‐ y Mn x Co y O 2 ) cathodes have been found to exhibit exceptional electrochemical properties when coupled with various inorganic solid electrolytes (ISEs) in all‐solid‐state batteries (ASSBs). Their advantages stem from the robust morphological integrity with the absence of grain boundaries and the high electrochemical oxidative stability. Here, ASSBs featuring single‐crystalline LiNiO 2 (LNO) with the highest Ni content are reported, offering a high theoretical specific capacity of 275 mAh g ‐1 alongside a high average discharge voltage (3.7 V vs Li + /Li). Through a careful investigation, it is demonstrated that micron‐sized single‐crystalline LNO (µSC‐LNO) composite cathodes with a halide ISE exhibit a high initial discharge capacity of 205 mAh g ‐1 with an outstanding cycle performance over 200 cycles in room‐temperature ASSBs. The significance of engineering parameters is emphasized, such as particle size and specific density, in promoting a homogeneous and fast Li + transport within the composite cathodes. Furthermore, the formation of undesirable interphase between the halide ISE in the cathode and sulfide ISE separator is elucidated, which may be a critical factor impeding long‐term cyclability of ASSBs. This work provides insights into the design of composite cathodes for high‐energy‐density ASSBs.

Chemistry

Radiation sensitivity of quartz crystal oscillators experiment for the Long Duration Exposure Facility (LDEF)

Factors determining the radiation sensitivity of quartz crystal oscillators were studied on NASA's LDEF. Quartz materials were examined in the transmission electron microscope (TEM) and classified as to their sensitivity to radiation damage by establishing the rate of damage caused by the electron beam in the microscope. Two types of materials, i.e., swept premium Q quartz and natural quartz were chosen because clear differences were observed in their response to the electron beam in the TEM studies. Quartz resonators were then fabricated from them, tested for frequency stability over a greater than 6 mo. period and flown on the LDEF satellite. After retrieval (more than 7 yrs in space) the stability of the resonators was again determined. All of the space exposed resonators fabricated with swept premium Q material exhibited a frequency shift above that of the control resonators: none of the resonators fabricated from the natural quartz materials exhibited such a shift. The significant differences observed between the two types of materials in both the ground-based TEM studies and the space radiation induced frequency changes suggest that there may be a correlation between the two observations.

J. S. Ahearn

Design and Optimization of an Open Rotor Stage

Open rotor propulsors enable greatly increased effective bypass ratios over current aircraft engines, resulting in significantly improved efficiencies. One of the most promising of these geometries is the “open fan”, which consists of a single rotor followed by a single stator. This configuration will be referred to as an “open rotor stage” for design work at NASA. In this work we consider the multidisciplinary design and optimization of an open rotor stage using a variety of 2D and 3D techniques. The 2D aerodynamic techniques used for design include a 2D Trefftz plane method, axisymmetric throughflow, and quasi-3D blade-to-blade CFD. Aerodynamic performance is prioritized, while structural requirements are met and some acoustic considerations are included. Between the rotor, stator, and hub profiles, a total of 101 design variables are used. Differences in the process of designing an open rotor stage vs. designing other high-speed propellers are also discussed. The current design, the NASA Optimized Propulsor for Efficiency and Noise (N-OPEN-1), achieves 84.7% net efficiency as predicted by 3D CFD, with further improvements expected to be possible. This design makes effective use of a slower rotor and a less tip-loaded work distribution than typical single-rotation propellers, allowing the stator to produce 14.8% of the thrust. Laminar flow on the blades was responsible for a 1.7% efficiency benefit and warrants further study.

turbomachinery

Achieving 20.1% Efficiency in Organic Solar Cells Through Interconnected Fibrillar Networks via Local Molecular Stacking

ABSTRACT The performance of organic solar cells (OSCs) is governed by how molecular packing evolves into interconnected networks that facilitate exciton dissociation and charge transport. Using an all‐small‐molecule blend DR3TSBDT:Y6 as a model system, we study how local molecular stacking evolves into performance‐relevant morphology during solvent vapor annealing (SVA) and subsequent thermal annealing (TA). SVA promotes end‐to‐end stacking of amorphous acceptors to form interconnected fibrils, while TA compacts inter‐fibril spacing without disrupting favorable local order. Such molecular‐to‐morphological refinements broaden light absorption, enhance charge transport, and markedly improve device efficiency. Extending this approach to additional blend systems (D18:Y6, D18:L8‐BO, and DR3TSBDT:L8‐BO) yields similar structural evolution and performance gains, with the D18:L8‐BO system achieving up to 20.10% PCE. Our study establishes control over local stacking in amorphous acceptors into fibrillar networks as a general and effective route to realize high‐performance OSCs.

Wu, Junying

Thermal Reservoir Networks for Modularly Expandable Thermal Microgrids

The Department of Defense (DoD) faces the substantial challenge of cost-effectively retrofitting one to two installations per month, each comprising approximately 1,000 buildings, to improve resilience, reduce energy consumption, and enhance energy supply security. Achieving these objectives requires optimal system selection and effective risk mitigation during system integration. To address this need, we introduce Platform-Based Design (PBD), a structured, hierarchical methodology adapted from other industrial sectors to the domain of energy system retrofits. We demonstrate the effectiveness of PBD through a techno-economic feasibility study comparing geothermal-coupled thermal energy networks (TENs) with conventional energy systems for heating, cooling, and powering 17 buildings at Joint Base Andrews (JBA) in Maryland. Our analysis illustrates that the PBD approach enables rigorous, data-driven, sequential decision making, resulting in a family of Pareto-optimal systems, among which the TEN emerged as the most promising solution. The selected TEN design integrates geothermal borefields, heat recovery heat pumps, photovoltaic (PV) arrays, and battery storage. Compared to the baseline system – gas heating combined with air-source chillers – the proposed TEN reduces annual imported energy by 74% and peak electricity demand by 45%, achieves a levelized cost of energy of $\$0.210$/kWh, and substantially enhances resilience. Life-cycle costs increase by approximately 6%, and initial investment costs are about 2.5 times higher than the baseline. However, if central plant infrastructure, district loops, and utility-scale PV and battery systems are privately funded and operated, the initial investment would fall below the baseline system cost. Critical to achieving these significant performance improvements were detailed nonlinear dynamic simulations coupling geothermal heat transfer, energy system operation, and realistic feedback control logic. These simulations identified essential design modifications and control strategy refinements that substantially reduced energy use, peak demand, and compressor shortcycling, thereby improving durability and reliability—issues that would have been significantly more expensive to resolve during operation. Additionally, the verification step highlighted sensitivities to key design parameters that could reduce initial investment by approximately $\$2$ million and reduce annual life-cycle costs more than $\$300,000$. We recommend adopting the PBD methodology for future feasibility studies and TEN pilot projects to gain valuable operational experience. Furthermore, we recommend that DoD invest in transferring and scaling the PBD methodology to other installations. This entails developing standardized computational frameworks and component libraries as well as training industry in conducting PBD. Such investments would enable rapid, robust, reliable, and cost-effective retrofits, supporting DoD’s ambitious energy system modernization goals.

Wetter, Michael [Lawrence Berkeley National Labora

Validation of the SINDA/FLUINT Code Using Several Analytical Solutions

The Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) code has often been used to determine the transient and steady-state response of various thermal and fluid flow networks. While this code is an often used design and analysis tool, the validation of this program has been limited to a few simple studies. For the current study, the SINDA/FLUINT code was compared to four different analytical solutions. The thermal analyzer portion of the code (conduction and radiative heat transfer, SINDA portion) was first compared to two separate solutions. The first comparison examined a semi-infinite slab with a periodic surface temperature boundary condition. Next, a small, uniform temperature object (lumped capacitance) was allowed to radiate to a fixed temperature sink. The fluid portion of the code (FLUINT) was also compared to two different analytical solutions. The first study examined a tank filling process by an ideal gas in which there is both control volume work and heat transfer. The final comparison considered the flow in a pipe joining two infinite reservoirs of pressure. The results of all these studies showed that for the situations examined here, the SINDA/FLUINT code was able to match the results of the analytical solutions.

John R Keller

Reconfigurable structural color by reversible switching of colloidal discoid liquid crystal alignment

Combining the effects of alternating-current (AC) electric fields and sedimentation reconfigures colloidal discoids between planar and homeotropic orientational alignments, thereby controlling the material’s structural color. Here, we self-assemble micrometer-size polystyrene discoids in an isopropanol-water mixture. After sedimentation, the discoids adopt a homeotropic alignment, with the minor axis perpendicular to the substrate. Adding an AC electric field (1 kHz) of ≥0.50 V switches the discoids to planar alignment—with the minor axis parallel to the substrate—within ∼100 s. Removing the field switches them back to homeotropic alignment within ∼300 s. Kinetic modeling of the field-induced torques yields good agreement with these measurements. The peak wavelength and intensity of the crystal’s diffraction response shift significantly upon reconfiguration; scattering simulation predicts these shifts. The reconfiguration is maintained for at least 10 cycles. This method is a simple, scalable avenue to reconfigure the optical properties of colloidal crystals produced from simple dielectric spheroids.

colloidal crystals

Collective behavior of “flexicles”

In recent years the functionality of synthetic active microparticles has edged even closer to that of their biological counterparts. However, we still lack the understanding needed to recreate at the microscale key features of autonomous behavior exhibited by microorganisms or swarms of macroscopic robots. In this study, we propose a model for a three-dimensional deformable cellular composite particle consisting of self-propelled rod-shaped colloids confined within a flexible vesicle—representing a superstructure we call a “flexicle” that couples particle deformation to the internal dynamics of the internal active components. Using molecular dynamics simulations, we investigate the collective behavior of dense systems composed of many flexicles. We show that individual flexicles exhibit shape changes upon collisions with other flexicles that lead to rearrangements of the internal active rods, which slows flexicle motion. This shape deformability gives rise to a diverse set of motility-induced phase separation phenomena and the spontaneous flow of flexicles reminiscent of the migration of cells in dense tissues. Our findings establish a foundation for designing responsive, cell-like active particles and developing strategies for controlling swarm migration and other autonomous swarm behaviors at cellular and colloidal scales.

Science & Technology - Other Topics

Project Development of an Electrochemical Denitration and Caustic Generation System for HLW Pretreatment at Hanford - 26350

An engineering-scale electrochemical processing skid is proposed to perform the denitration of Hanford tank waste, which would help to mitigate a key process concern with the direct feed processing of the Hanford Tank Waste Treatment and Immobilization Plant (WTP). The reduction of nitrates and organic compounds in the waste feed will directly reduce hazardous NOx and ammonia gases generated during the vitrification process, which in turn will aid in addressing potential regulatory and safety challenges associated with processing large volumes of tank waste. This paper highlights the past legacy work, project layout, accomplishments from Phase 1 and research and development envisioned for Phase 2. An innovative electrochemical denitration and caustic generation (EDCGe) process was demonstrated for the pretreatment of tank waste at the Savannah River Site (SRS) in the early 2000s. The denitration electrolyzer, off-gas abatement system, and caustic generator electrolyzer are being developed with the intent that the denitration electrolyzer will convert nitrate and nitrite anions to nitrogen gas while also yielding other gaseous byproducts, which may include N2O, NH3, VOCs, and H2. The gaseous byproducts will be managed via a tandem off-gas catalyst-bed treatment system. The caustic generation electrolyzer will recycle NaOH from the feed to produce a clean caustic stream for use within the batching tanks at Hanford, aiding in the preparation of waste for WTP. The reduction in hazardous emissions and improved waste treatment processes provides a robust solution for nuclear waste management, contributing to environmental safety and regulatory compliance. The EDCGe technology is being adapted, modified, and updated for the preparation of the Direct Feed-High Level Waste (DF-HLW) flowsheet at Hanford. Phase 1 demonstrated a bench-scale proof-of-concept for reactions involving the denitration electrolyzer and gas phase abatement of ammonia. The electrochemical technology is drawing on the scientific outcomes that were reported in the legacy work. The results from Phase 1 demonstrated the viability of the EDCGe system in reducing the nitrogen species of simple non-radioactive waste simulants. Commercially available alloys used as electrode materials and membranes are being studied for the denitration and caustic generation electrolyzers. The continuation of this project holds promise for broader applications, such as energy-efficient ammonia production, and contributes significant advancements in nuclear waste management. Additional material discovery has been investigated into ceramic Na super ion conductive (NaSICON) materials and off-gas abatement catalyst discovery. NaSICON is of interest for selective transport of Na within the electrolyzers to make a clean caustic stream. Future integration and optimization efforts, informed by Phase 1 results and ongoing research, will continue to drive advancements in nuclear waste management technology. The technology developed for the EDCGe treatment of tank waste will also have broader potential to inform other fields, such as energy-efficient ammonia production, as well as ammonia abatement catalysis through the lessons learned in electrochemical nitrate reduction. The applications and benefits of this research extend beyond Hanford and the Savannah River Site, supported by a collaborative team of scientists and engineers from national labs, academia, and industry, ensuring a comprehensive approach to solving complex waste treatment challenges. The team is leveraging advanced electrochemical technologies, machine learning, novel catalysts tailored for gaseous nitrogen species, and cutting-edge reactor systems to enhance the process efficiency and effectiveness of the denitration process.

Rodene, Dylan [Savannah River National Laboratory

Long-range magnetic order and relaxor ferroelectricity in a hexagonal high-entropy ferrite

Multiferroics that combine ferroelectricity and magnetic order are attractive for electronic and spintronic technologies, yet chemical disorder that promotes relaxor ferroelectricity usually suppresses long-range magnetic order. Here, we report entropy-stabilized relaxor multiferroicity in epitaxial hexagonal (Tb0.2Dy0.2Ho0.2Lu0.2Yb0.2)FeO3 thin films. Structural, magnetic, dielectric, and synchrotron spectroscopic measurements show the coexistence of relaxor ferroelectricity and long-range ferromagnetic order. We find that improper ferroelectricity remains robust against A-site configurational disorder, while the Fe sublattice preserves magnetic exchange. This separation of the microscopic origins of the polar and magnetic responses enables chemically disordered multiferroicity. Our results establish entropy engineering in hexagonal ferrites as a route toward multifunctional oxide thin films and provide a general design strategy for high-entropy multiferroics.

Miertschin, Duncan [Baylor University]

Equivalent System Mass Comparison of ECLSS CO2 Removal Technologies

This project employs equivalent system mass (ESM) analyses to evaluate and compare state-of-the-art spacecraft CO2 removal systems. The ESM methodology converts sizing characteristics such as volume, power, and cooling requirements into a unified metric of mass, allowing for simple quantitative comparison of equipment impacts on a system level. Comparison of six high TRL technologies – the Carbon Dioxide Removal System (CDRS), Thermal Amine Scrubber (TAS), Carbon Dioxide Removal Assembly (CDRA), Four-Bed CO2 Scrubber (4BCO2), CO2 and Humidity Control Swing Bed (CHC), and the Carbon Dioxide Removal by Ionic Liquid Sorbent (CDRILS) – was achieved using an existing ESM spreadsheet tool that formerly ranked such technologies for consideration on Gateway. Fidelity of the tool was increased through revision with the most up-to-date sizing and performance data for each technology. ESM values were then estimated using NASA-supplied Lunar, Martian, and low-Earth orbit habitat infrastructure costs. This paper details the ESM approach used, lists major performance variables for each CO2 removal option, and summarizes conclusions of the technology comparison. The results are intended to act as a guide to assist programs in their selection of CO2 technologies best suited for a specific vehicle or mission.

Madeleine C Oliver

A Probabilistic Approach to Load Modeling for Central HVAC Systems in Large Commercial Buildings for Retrofit Decisions Under Uncertainty

Retrofitting central HVAC systems in large commercial buildings with advanced technologies like heat recovery chillers (HRCs) offers a significant opportunity to enhance energy efficiency. However, analyzing these retrofits is challenging with traditional whole-building simulation tools, which require intensive calibration and struggle to model innovative system configurations and controls. To overcome these limitations, this study proposes a load profilebased retrofit analysis framework that provides better decisions under uncertainty. The main focus of this paper is the development of a probabilistic load profile model that can be used in the framework by using exploratory data analysis (EDA) of measured building data to properly quantify its inherent variability. A non-parametric Gaussian Process (GP) model was employed to capture the time- and weather-dependent characteristics of the heating load while explicitly modeling its uncertainty. The model's effectiveness is demonstrated through strong predictive performance on unseen data and physically interpretable insights into load behavior. This data-driven, probabilistic load profile serves as a robust and flexible input for subsequent system simulations, enabling a more confident and statistically sound analysis of retrofit potential.

Ham, S W

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING