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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 OSTI2022

Optimization of the moderators in the STS preliminary design

This report details the results for an optimization of the dimensions of the moderators in the preliminary design of the Spallation Neutron Source Second Target Station (STS). This study uses the optimization algorithms of Dakota and an unstructured mesh model for the moderators in MCNP. More details on the unstructured mesh model and the automated mesh generation can be found in [3]. Parallel to this effort, the same moderator geometries have been optimized using a constructive solid geometry (CSG) MCNP model. More details on this model and its results can be found in [4]. Three optimal designs are selected for each moderator: one that is optimized for maximum peak brightness, one for maximum time-integrated brightness, and one for a combination of peak and time-integrated brightness. The backbone of the optimization work flow is provided by Dakota. For each set of design parameters requested by Dakota, a new solid geometry is automatically built in Creo and SpaceClaim, and subsequently exported to Attila4MC to generate an unstructured mesh geometry for MCNP. After the MCNP calculation is finished, the objective function (e.g., brightness metric) is returned to Dakota. After the new design has been evaluated, a result-file is written, and Dakota proposes the next set of design parameters to be evaluated. The loop continues until a specified convergence criterion has been met. The design parameters of the cylindrical (upper) moderator include the hydrogen radius, the premoderator thickness (top, bottom, radial), the beryllium radius and the horizontal position of the moderator. The crucial design choice is the hydrogen radius. A radius of 62 mm is shown to provide the maximum time-integrated brightness. The maximum peak brightness occurs with a radius of 40 mm. A combined (middle) design, which balances peak and time-integrated brightnesses, is obtained with a hydrogen radius of 50 mm. The premoderator thicknesses and the beryllium radius are slightly larger in the design optimized for time-integrated brightness than in the design optimized for peak brightness. The sensitivity to these two parameters is relatively small close to the optimal configurations. The hydrogen vessel and vacuum vessel wall thicknesses are dependent on the radius of the liquid hydrogen due to structural integrity requirements. The increased wall thicknesses for larger vessels significantly penalize the time-integrated brightness, with the maximum obtainable value reduced by more than 10% relative to earlier studies which used fixed vessel wall thicknesses. The impact of the variable wall thicknesses is much less for the peak brightness and combined brightness designs. The design parameters of the tube (lower) moderator selected for the optimization are the tube length, the annular premoderator thickness, the beryllium radius and the horizontal position of the moderator. The tube length is the crucial parameter and is chosen large (210 mm) and small (125 mm) in the designs optimized for time-integrated and peak brightness respectively. A combined optimal design has a tube length of 170 mm. The premoderator thickness and the beryllium radius are chosen larger in the design optimized for time-integrated brightness.

42 ENGINEERING↗
DOE OSTI2024

On the cogent formulation of an elastomeric silicone ink material for direct ink write ( DIW ) 3D printing

Abstract Adhesives and sealants show fine rheology with good physical and mechanical properties as viscous pastes, a possible starting point for developing direct ink writing (DIW) 3D printing ink. However, many commercial adhesives and sealants take days or weeks to cure fully. DIW 3D‐printed parts made directly from these sealants are not designed for a scalable manufacturing process and high‐volume production. Moreover, most of these adhesives and sealants have volume shrinkage during cure. A systematic understanding of formulation methods and design principles for an elastomeric silicone DIW ink can overcome these issues. This study presents the cogent formulation development of a 3D printable thermoset elastomer silicone that gels and cures isotropically in minutes, reducing cycle time for rapid ink development with no shrinkage during cure. More specifically, we outline the principles of raw material selection of a formulation to achieve excellent rheology, printability, synchronized working, and gel time fitting requirements closer to scalable manufacturing. The reaction kinetics and their corresponding 3D‐printed structural properties are also described. Interest in future work is toward a rational DIW 3D printing ink material development protocol and use of machine learning (ML). Highlights Formulation method flexibility and design principle of DIW ink. Raw material selection principle to achieve optimal rheology for DIW printing. Ink gel kinetics for large‐scale DIW manufacturing. Hydrosilylation conversion over time at different ambient temperatures. Structural properties of DIW 3D printed parts.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Optimal Design and Techno-Economic Analysis of 3D-Printed, Intensified Packings for Absorbers and Strippers in Solvent-Based CO 2 Capture

A potential technology for the CO 2 absorption process is utilizing intensified structured packing with embedded cooling/heating channels for continuous heat exchange, which can overcome limitations of discrete methods, such as discrete intercooling and centralized reboilers, to aid in reducing energy consumption and decreasing costs. This work investigates the modeling of intensified packing (IP) for the stripper tower, extending on previous work for the absorber, which distributes heat internally within the column, improving the thermodynamics for the solvent regeneration process. The model includes submodels for steam turbine extraction to produce steam at various qualities as well as a surrogate model for calculating steam enthalpy. A cost model for a plant-scale absorption capture process was developed, allowing for the design of the plant to be optimized, subject to minimizing capture cost using two different power plant flue gas sources. In this optimization, the placement of IP in both towers is optimized to balance the trade-off between enhanced heat transfer and reduced mass transfer volume. For natural gas combined cycle flue gas, the standard process configuration had a minimum cost of $\$$65.40/tonne CO 2 , and considering IP, the minimum capture cost is reduced to $\$$62.73/tonne, with utilization in the stripper column, which reduces yearly costs by up to $\$$2.67 MM/yr. Cooling the absorber through IP, or intercoolers, was only found to be beneficial at higher capture rates, with IP in both towers having a cost of capture of $\$$68.08/tonne at 99.9% capture, a reduction of $\$$12.64/tonne when using only intercoolers at the same capture rate. When capturing from pulverized-coal power plants, the minimum cost of capture when using IP in both towers is $\$$44.18/tonne (at 97% capture), while the standard configuration with and without intercoolers was $\$$45.69 and $\$$47.22 per tonne, respectively. This results in a reduction in yearly costs of $\$$16.98 MM/yr from the base-case configuration. At this higher CO 2 concentration, cooling in the absorber from the IP becomes extremely beneficial, reducing energy consumption by up to 6%.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2023

Navigating the Expansive Landscapes of Soft Materials: A User Guide for High-Throughput Workflows

Synthetic polymers are highly customizable with tailored structures and functionality, yet this versatility generates challenges in the design of advanced materials due to the size and complexity of the design space. Thus, exploration and optimization of polymer properties using combinatorial libraries has become increasingly common, which requires careful selection of synthetic strategies, characterization techniques, and rapid processing workflows to obtain fundamental principles from these large data sets. Herein, we provide guidelines for strategic design of macromolecule libraries and workflows to efficiently navigate these high-dimensional design spaces. We describe synthetic methods for multiple library sizes and structures as well as characterization methods to rapidly generate data sets, including tools that can be adapted from biological workflows. We further highlight relevant insights from statistics and machine learning to aid in data featurization, representation, and analysis. This Perspective acts as a “user guide” for researchers interested in leveraging high-throughput screening toward the design of multifunctional polymers and predictive modeling of structure–property relationships in soft materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Distinguishing photo-induced oxygen attack on alkyl chain versus conjugated backbone for alkylthienyl-benzodithiophene (BDTT)-based push–pull polymers

Synthetic design has enabled increasing power conversion efficiency advances in organic photovoltaics (OPV). One continuing knowledge gap is detailed understanding of single-material chemical (photo)stability. Many considerations are based on prior OPV-relevant donor homopolymer systems rather than the next-generation push–pull architectures. Generally, energetic offsets between the lowest occupied molecular orbital of the donor and molecular oxygen are assumed to dictate kinetics of photo-induced charge transfer to a super oxide radical. Herein we determine the ambient-induced photo-degradation pathways, presented as proposed site-specific arrow-pushing mechanisms, for five donor polymers all containing the same push unit – alkylthienyl-substituted-benzodithiophene (BDTT) – but with chemically distinct pull units. The donor-only polymer films were subject to controlled photobleaching in air as an accelerated degradation approach, coupled with simultaneous monitoring of absorptance. Sample subsets were periodically removed and analyzed with X-ray photoelectron spectroscopy, to evaluate near-surface chemical composition and oxygen additions to hetero reporter atoms on either the BDTT push unit or distinct pull unit (i.e., sulphur and nitrogen). Here, this methodology allows us to distinguish between different mechanisms of bond cleavage and formation. Overall, we find that neither polymer redox properties nor individual push or pull unit stability are sufficient to predict photo-oxidative degradation of these polymers. Rather, there is a greater dependence on the susceptibility of unique structural groups within a polymeric system. Alkyl chain oxygen addition is generally the first attack site and direct sulfur oxidation on the conjugated backbone occurs after saturation of the alkyl chain initiation sites. This work provides a standard that could be used to evaluate relative photo-oxidative (in)stability for new OPV materials quickly – prior to time-consuming device optimization – and demonstrates an effective methodology for correlating optical degradation with chemical structure alterations via spectroscopic signatures to guide synthetic design.

14 SOLAR ENERGY↗
DOE OSTI2024

Development of Lightweight Structural Materials with Improved Properties for Fission Batteries

The notion of a “fission battery” conveys a vision focused on realizing very simple “plug-and-play” nuclear systems that can be integrated into a variety of applications requiring affordable, reliable energy in the form of electricity and/or heat and function without operations and maintenance staff. Fission batteries require lightweight structural materials to increase their mobility, and the lightweight materials must demonstrate structural resilience under various conditions. The objective of this work is to develop lightweight structural material featuring a good combination of mechanical properties using advanced modeling and simulation together with an advanced additive manufacturing technique such as laser powder bed fusion. The preliminary results show that different lattice structures and types can be successfully meshed using nTopology software, and the lattice structure data can be successfully transformed to Multiphysics Object-Oriented Simulation Environment (MOOSE) input. Finite Element Analysis (FEA) displays that, at macro/engineering scale simulation, the weight saving design has an obvious effect on tensile behavior such as effective elastic modulus and yield stress. The novel approaches of this work are (1) development of optimized lattice structures for improved mechanical properties using advanced simulation and modeling techniques; and (2) model predictions of the mechanical properties (e.g., strength and stress distribution) of macroscopic materials in order to preliminarily select a lattice structure for additive manufacturing.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Grand canonical inverse design of multicomponent colloidal crystals

Inverse design methods are powerful computational approaches for creating colloidal systems which self-assemble into a target morphology by reverse engineering the Hamiltonian of the system. Despite this, these optimization procedures tend to yield Hamiltonians which are too complex to be experimentally realized. An alternative route to complex structures involves the use of several different components, however, conventional inverse design methods do not explicitly account for the possibility of phase separation into compositionally distinct structures. We present an inverse design scheme for multicomponent colloidal systems by combining active learning with a method to directly compute their ground state phase diagrams. This explicitly accounts for phase separation and can locate stable regions of Hamiltonian parameter space which grid-based surveys are prone to miss. Using this we design low-density, binary structures with Lennard-Jones-like pairwise interactions that are simpler than in the single component case and potentially realizable in an experimental setting. This reinforces the concept that ground states of simple, multicomponent systems might be rich with previously unappreciated diversity, enabling the assembly of non-trivial structures with only few simple components instead of a single complex one.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Computational design of thermoelectric alloys through optimization of transport and dopability

Alloying is a common technique to optimize the functional properties of materials for thermoelectrics, photovoltaics, energy storage etc. Designing thermoelectric (TE) alloys is especially challenging because it is a multi-property optimization problem, where the properties that contribute to high TE performance are interdependent. In this work, we develop a computational framework that combines first-principles calculations with alloy and point defect modeling to identify alloy compositions that optimize the electronic, thermal, and defect properties. We apply this framework to design n-type Ba 2(1–x) Sr 2x CdP 2 Zintl thermoelectric alloys. Our predictions of the crystallographic properties such as lattice parameters and site disorder are validated with experiments. To optimize the conduction band electronic structure, we perform band unfolding to sketch the effective band structures of alloys and find a range of compositions that facilitate band convergence and minimize alloy scattering of electrons. Here, we assess the n-type dopability of the alloys by extending the standard approach for computing point defect energetics in ordered structures. Through the application of this framework, we identify an optimal alloy composition range with the desired electronic and thermal transport properties, and n-type dopability. Such a computational framework can also be used to design alloys for other functional applications beyond TE.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Predicting the onset of metal-insulator transitions in transition metal oxides-A first step in designing neuromorphic devices.

Several transition metal oxides, including La1-xSrxCoO3, are promising materials to realize resistive switching devices for neuromorphic applications, as they can undergo a metal-to-insulator transition (MIT) upon small perturbations to their electronic structure. Here, we focus on the MIT induced by varying the oxygen vacancy concentration, and we propose a model to predict the required electrical bias, based on three fundamental quantities: the vacancy formation energy, the permanent polarization in the material, and its dielectric constant. We obtain these quantities using first-principles electronic structure calculations, and we discuss strategies to minimize the electrical bias which may be adopted experimentally to design and optimize neuromorphic devices.

Zhang, Shenli↗
DOE OSTI2025

Dynamical Ion Correlations in Polymer and Membrane Electrolytes: Recent Advances and Open Questions

Ion transport in polymer and membrane electrolytes is often described using uncorrelated models like the Nernst–Einstein (NE) approximation, which link conductivity, transference number, and salt diffusivity to individual ion mobilities. However, growing evidence shows that dynamical ion correlations─arising from ion pairing, polymer-mediated coupling, confinement, and electrostatic interactions─can substantially alter macroscopic transport properties. The Onsager transport formalism offers a rigorous framework to quantify these effects via cross-correlated ionic displacements. This Perspective highlights how such correlations manifest across dry and hydrated systems, including salt-doped polymers, block copolymers, hydrogels, and ion-exchange membranes. Here, we examine key physical origins, the influence of salt chemistry and polymer structure, and open questions in measuring and controlling correlated motion. Embracing correlation-aware design enables new pathways to optimize conductivity, transference number, and selectivity─shifting the focus from individual ion mobility to engineered collective dynamics for next-generation electrolytes in energy storage and separations.

Charge transport↗
DOE OSTI2025

Evaluating the Origins of Aerobic Oxidation Catalysis with TAM-3, a MOF with Accessible Co(II) Sites and Large Pores

Metal-organic frameworks (MOFs) are attractive platforms that merge concepts of homogeneous and heterogeneous catalysis. Catalyst design and optimization are enabled by an array of synthetic methods that offer independent control over the local chemical structure of lattice-embedded metal ions (i.e., ligand identity and geometry) and the long-range materials properties (i.e., porosity). Establishing the origin of catalytic activity in MOF-promoted reactions remains a significant challenge: The relative rates of catalyst turnover and substrate diffusion dictate the extent to which interstitial sites are accessible and operational in catalysis. To minimize the contributions of surface sites in catalysis, materials with large pore dimensions are often sought, however, the impact of pore expansion on the origins of catalytic activity is similarly challenging to establish. Here, we describe TAM-3, a Co(II) based MOF with accessible metal sites supported by a facially coordinating tris-tetrazole ligand set. TAM-3 features large channel-like pores (17 × 23 Å) and promotes aerobic C−H oxidation and olefin epoxidation. Using a set of simple kinetics experiments, based on the analysis of kinetic isotope effects and olefin oxidation diastereoselectivities, we demonstrate that despite the large pores, interstitial metal ions do not significantly contribute to the observed substrate oxidation. This study highlights the importance of conducting kinetic experiments to assess the origin of apparent catalytic activity with MOFs and the challenge of harnessing reactive oxidants with microporous catalyst materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Elucidating Compositional Differences in Halide Perovskites for Normal and Inverted Perovskite Solar Cells

Over the recent few years, extensive research efforts have shifted from normal (n-i-p) to inverted (p-i-n) perovskite solar cells (PSCs), owing to their promising efficiency and operational stability, enabled by low-temperature processing. Despite a fundamentally identical operation principle (only structurally inverted), the optimized perovskite compositions for normal and inverted PSCs differ significantly across the literature, suggesting an underlying design principle for perovskite composition. Here, we unveil the role of cesium cation in enhancing interfacial contact between the perovskite layer and the underlying hole-transporting layer (HTL) in inverted PSCs. Comprehensive in situ and device characterization reveal that cesium incorporation promotes the formation of initial nucleation seeds for heterogeneous nucleation at the perovskite/hydrophobic HTL interface, thereby improving their contact. The resulting compositional heterogeneity explains the focus of recent studies on resolving this issue. This study provides mechanistic insight into designing perovskite compositions to further enhance the performance and longevity of PSCs.

Park, Keonwoo↗
DOE OSTI2022

Additive manufacturing of LiNi 1/3 Mn 1/3 Co 1/3 O 2 battery electrode material via vat photopolymerization precursor approach

Additive manufacturing, also called 3D printing, has the potential to enable the development of flexible, wearable and customizable batteries of any shape, maximizing energy storage while also reducing dead-weight and volume. In this work, for the first time, three-dimensional complex electrode structures of high-energy density LiNi 1/3 Mn 1/3 Co 1/3 O 2 (NMC 111) material are developed by means of a vat photopolymerization (VPP) process combined with an innovative precursor approach. This innovative approach involves the solubilization of metal precursor salts into a UV-photopolymerizable resin, so that detrimental light scattering and increased viscosity are minimized, followed by the in-situ synthesis of NMC 111 during thermal post-processing of the printed item. The absence of solid particles within the initial resin allows the production of smaller printed features that are crucial for 3D battery design. The formulation of the UV-photopolymerizable composite resin and 3D printing of complex structures, followed by an optimization of the thermal post-processing yielding NMC 111 is thoroughly described in this study. Based on these results, this work addresses one of the key aspects for 3D printed batteries via a precursor approach: the need for a compromise between electrochemical and mechanical performance in order to obtain fully functional 3D printed electrodes. In addition, it discusses the gaps that limit the multi-material 3D printing of batteries via the VPP process.

25 ENERGY STORAGE↗
DOE OSTI2025

A Probabilistic Reasoner Based on Bayes Risk for Damage Detection in Structural Systems

Structural health monitoring (SHM) systems are used to inform operation of structural systems subject to loads and environments that may affect their integrity. SHM systems rely on continuous monitoring of the structure to determine its health state. These systems are often coupled with a model of the deployed structure to determine the consequences of changes in the system by forecasting the response to future states. These models, which may be thought of as digital twins, need to be updated to reflect the latest state of the structural system. This work makes use of an uncertainty-aware machine learning model that enforces distance preservation of the original input space to determine deviations from the training data input space distributions. This workflow enables domain shift detection to determine whether damage is present in the structure. The uncertainty metrics generated by this network are then used in a Bayes risk framework to design an optimal damage detector given cost and risk considerations. The approach is demonstrated on a computational example with simulated damage.

Najera-Flores, David [ATA Engineering, Inc.]↗
DOE OSTI2020

Use of in Situ Synchrotron Techniques to Probe the Oxidized Surface of Molybdenum Nitride Oxygen Reduction Electrocatalysis

The development of active and stable earth-abundant catalysts for the oxygen reduction reaction (ORR) is needed for widespread, economic development of fuel cell technologies. Designing and optimizing these non-platinum group metals is challenging, however, because they are susceptible to composition and structure changes, including dissolution, oxidation, and corrosion, both in air and under reaction conditions. To identify the active surface, and thus understand the properties that affect activity, the catalyst surface must be characterized in situ. Herein, we utilize a grazing incidence electrochemical cell to investigate in situ composition and morphology changes of a molybdenum nitride (Mo-N) thin film catalyst using grazing incidence x-ray absorption spectroscopy (GI-XAS) and x-ray reflectivity (XRR). In rotating ring disk electrode measurements, we find that the activity, selectivity, stability, and capacitance of the Mo-N catalyst is dependent on the maximum potential to which it has been exposed. Specifically, the overpotential required to reach -2 mA cm-2geo decreases by over 90 mV when the maximum potential is increased from 0.3 to 0.8 V vs RHE (Figure 1). Because the Mo-N oxidizes rapidly in air, ex situ characterization methods including x-ray photoelectron spectroscopy and time-of-flight secondary ion mass spectrometry can provide only limited insight into these in situ catalyst changes. Using in situ GI-XAS measurements at applied potentials between 0.3 and 0.9 V vs RHE, however, we are able to determine that the surface of the film oxidizes and becomes more amorphous when exposed to increasingly higher potentials (Figure 1). Furthermore, the surface remains oxidized on the order of several hours when returned to "ORR relevant potentials" (< 0.6 V vs RHE), indicating that this surface-oxidized nitride is the active surface for ORR. Using in situ XRR measurements, we find that there is no change in surface roughness at potentials below 0.7 V vs RHE, but the film roughens significantly at 0.8 V vs RHE, correlating with ex situ measurements of Mo dissolution at this potential (Figure 1). We therefore conclude that the intrinsic activity of the Mo-N catalyst increases when exposed to potentials up to 0.7 V vs RHE, while above that potential activity enhancements are due to the exposure of more active sites through dissolution. The in situ electrochemical surface-sensitive x-ray characterization as used here is a promising methodology for understanding and leveraging surface dynamics to improve the performance of non-traditional catalysts.

Kreider, Melissa↗
DOE OSTI2025

A geometric framework for momentum-based optimizers for low-rank training

Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers such as heavy ball momentum methods or Adam. In this work, we identify and analyze potential difficulties that these training methods encounter when used to train low-rank parameterizations of weights. In particular, we show that classical momentum methods can struggle to converge to a local optimum due to the geometry of the underlying optimization landscape. To address this, we introduce novel training strategies derived from dynamical low-rank approximation, which explicitly account for the underlying geometric structure. Our approach leverages and combines tools from dynamical low-rank approximation and momentum-based optimization to design optimizers that respect the intrinsic geometry of the parameter space. We validate our methods through numerical experiments, demonstrating faster convergence, and stronger validation metrics at given parameter budgets.

Schotthoefer, Steffen [ORNL] (ORCID:00000002156965↗
DOE OSTI2023

Solar‐Driven CO 2 Conversion via Optimized Photothermal Catalysis in a Lotus Pod Structure

Abstract Photothermal CO 2 reduction is one of the most promising routes to efficiently utilize solar energy for fuel production at high rates. However, this reaction is currently limited by underdeveloped catalysts with low photothermal conversion efficiency, insufficient exposure of active sites, low active material loading, and high material cost. Herein, we report a potassium‐modified carbon‐supported cobalt (K + −Co−C) catalyst mimicking the structure of a lotus pod that addresses these challenges. As a result of the designed lotus‐pod structure which features an efficient photothermal C substrate with hierarchical pores, an intimate Co/C interface with covalent bonding, and exposed Co catalytic sites with optimized CO binding strength, the K + −Co−C catalyst shows a record‐high photothermal CO 2 hydrogenation rate of 758 mmol g cat −1 h −1 (2871 mmol g Co −1 h −1 ) with a 99.8 % selectivity for CO, three orders of magnitude higher than typical photochemical CO 2 reduction reactions. We further demonstrate with this catalyst effective CO 2 conversion under natural sunlight one hour before sunset during the winter season, putting forward an important step towards practical solar fuel production.

Wang, Hongmin↗
DOE OSTI2020

The potential of quantum annealing for rapid solution structure identification

Abstract The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing’s performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

97 MATHEMATICS AND COMPUTING↗