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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Lattice Boltzmann Method for Predicting Porous Transport Layer Performance During Electrolysis

Electrolysis, the splitting of water into oxygen and hydrogen using electricity, is a sustainable way to produce green hydrogen for energy storage. In polymer electrolyte membrane (PEM) water electrolysis, water is brought into contact with charged catalyst layers and electrochemically separated into oxygen and hydrogen. The hydrogen product formed at the cathode is carried through the catalyst layer for eventual collection, while the oxygen by-product formed at the anode is removed from the surface via a multiphase interaction with circulating water and a solid porous transport layer (PTL). The design of this PTL aids in the detachment and advection of the oxygen by-product and thereby plays a role in the overall efficacy of the catalyst. In this presentation, we present our initial results modeling this multiphase system using a single-component, multiphase lattice Boltzmann method. We use the Shan-Chen model describing inter-particle forces to capture both the cohesion of the water (liquid) and oxygen (gas) phases and their interaction with the PTL (solid) (Shan and Chen, 1993). We use a Carnahan-Starling equation of state to model the effective density governing these inter-particle interactions which allows us to model this relatively high density ratio system (Carnahan and Starling, 1969). With these simulations, we show that the geometry and heterogeneity of the PTL geometry plays a large role in its ability to move oxygen away from the catalyst layer and the resulting bubble structures that are formed within the PTL. The current work demonstrates these effects using synthesized PTL geometries and 2D physics, which will be extended to experimentally-imaged PTL sections and 3D algorithms in the near future.

Boltzmann↗
DOE OSTI2022

Device-Centric Ransomware Detection using Machine Learning-Based Memory Forensics for Smart Inverters

Ransomware attacks are the fastest-growing form of cyberattacks worldwide. Recently, ransomware attacks have targeted industrial control systems (ICSs), including power grids. Lessons learned from recent incidents in ICSs show that ransomware groups can deliver ransomware into not only the organization’s control servers, but also the operational technology (OT) devices such as smart inverters and smart grid devices. This paper proposes a machine learning (ML)- based memory forensics method enabling the detection of ransomware binaries stored in the memory of a commercial smart inverter. Device firmware binary files are extracted from a Serial Peripheral Interface (SPI) flash memory, and samples of both benign and ransomware binaries are generated by a binary manipulation method and a real-world ransomware encryption, separately. A deep transfer learning (DTL) method is used to retrain a convolutional neural network (CNN)-based ransomware detection algorithm using the generated samples. The experimental result validates that the proposed ML-based memory forensics method can accurately detect ransomware files.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Windowed Fourier transform and cross-correlation algorithms for molecular tagging velocimetry

In this study, simulated and experimental molecular tagging velocimetry (MTV) images have been analyzed with a technique commonly used to process grid images on surfaces, the windowed Fourier transform with local spectrum analysis (WFT-LSA). A systematic synthetic image study of the modulation transfer function (MTF) and error tendencies of the WFT-LSA was performed and compared with a PIV-style cross-correlation algorithm to see if advanced strategies such as iterative image deformation can improve analysis of gridded images with high noise levels. Testing of single-pass algorithms showed that in typical MTV images, the WFT-LSA yields significantly lower bias errors than cross-correlation (CC) at displacements greater than 1 pixel but slightly higher random error at all displacements and image conditions. Analysis of the MTF shows that CC provided better resolution of spatial fluctuations than the WFT-LSA in many combinations of grid size and interrogation window. Tests of image deformation algorithms showed that the gap in performance between CC and WFT-LSA is maintained even as both methods improve. Additionally, WFT-LSA and CC methods are applied to real MTV experiments in high-speed gas jet flows. A preliminary analysis of phosphorescence lifetime provided by acetone vapor excited at 266 nm is used for assessing the required gas speeds for making MTV application feasible. The application of WFT-LSA to real MTV images demonstrates the ability of the algorithm to handle further real-world effects that could not be considered in the synthetic image analysis, like reduced signal-to-noise ratio and non-uniform intensity of the tagging grid across the image introduced by the actual laser beam energy distribution. With experimental images, CC is more accurate with shear flows but less robust to high noise levels than WFT-LSA, as predicted by the synthetic image analysis.

42 ENGINEERING↗
DOE OSTI2025

Designing an Optimal Sensor Network via Minimizing Information Loss

Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting for the temporal dimension in our modeling and optimization. We observe that recent advancements in computational sciences often yield large datasets based on physics-based simulations, which are rarely leveraged in experimental design. We introduce a novel model-based sensor placement criterion, along with a highly-efficient optimization algorithm, which integrates physics-based simulations and Bayesian experimental design principles to identify sensor networks that “minimize information loss” from simulated data. Our technique relies on sparse variational inference and (separable) Gauss-Markov priors, and thus may adapt many techniques from Bayesian experimental design. We validate our method through a case study monitoring air temperature in Phoenix, Arizona, using state-of-the-art physics-based simulations. Our results show our framework to be superior to random or quasi-random sampling, particularly with a limited number of sensors. We conclude by discussing practical considerations and implications of our framework, including more complex modeling tools and real-world deployments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Multi-Source Machine Learning and Thermoplastics Enhanced Aerostructure Manufacturing (mTEAM)

RTX Technology Research Center (RTRC), together with Collins Aerospace (Collins) and Oak Ridge National Laboratory (ORNL) has developed an Artificial Intelligence (AI) / Machine Learning (ML) guided solution to advance the manufacturing and assembly of high performance and lightweight thermoplastic composite (TPC) aerospace products. The solution aims to lower risk, cost and lead time for induction heating based welding and consolidation processes for TPC structure. The cost and lead time of part and material specific process development for induction welding (IW) and induction consolidation will be reduced by replacing traditional empirical methods with optimization methods that merge AI/ML and physics-based process simulations and process experiments with sensing and controls. TPC-IW process development is empirical in nature, and uncertainties in material & process behavior exist near & far from the induction coil. Physics-based simulations can be leveraged directly for process optimization but can be too computationally expensive to run in high fidelity and real time to do robust process optimization. The key impact of successful TPC induction consolidation and welding is cost & lead time reduction for part & material specific consolidation and welding recipes. This is an enabler for more rapid deployment of TPC structures via joining assembly, which can reduce energy & cost intensive usage of autoclaves & ovens. The solution aimed to advance the U.S. Department of Energy’s interests in using thermoplastics and automation in composite manufacturing for improvement of products for existing markets via increased production speeds, reduced costs, and lowered use of energy. Welded TPC structures can offer significant weight & energy savings for high-value commercial aerospace & industrial applications compared to metal & thermoset composite structures assembled by mechanical fastening and/or adhesive bonding. The project was organized into two Budget Periods. Budget Period 1 (BP1) was 15 months and its goal was to perform ML process optimization framework development & deployment on lab-coupon aerostructure components. A Go/No-Go Review was performed at the end of BP1 to verify fulfilment of key tasks & milestones to justify a Go Decision to move into the next Budget Period. Budget Period 2 (BP2) was 12 months and its goal was the deployment of the ML framework for ML process optimization of pilot industrial scale aerostructure components. The overall project aim was to develop & demonstrate ML-enhanced modeling framework that learns process-property mapping from multiple data sources at different fidelities. During BP1, the team accomplished key tasks & milestones to demonstrate the concept of multi-source ML for TPC aerostructure consolidation and assembly. First, the team completed documentation of induction based TPC heating requirements including baseline metrics to compare measured results against. Next the team completed demonstration of data generation from physics-based simulations for ML surrogate model generation and demonstrated the integration of physics-based simulation data into multi-source AI/ML algorithms. In parallel, the team established the lab-coupon scale induction welding system and completed a process to label and reduce generated data from physics-based simulation and experiments for ML surrogate models to enable multi-source ML model training & testing. To complete BP1, the team integrated physics-based simulation data and experimental data into multi-source ML algorithms. This was based on the team completing ML deployment of the induction welding on a lab system at RTRC and AI/ML deployment on existing induction welding line at Collins. ORNL visited both Collins and RTRC sites to witness the TPC induction welding process. Then, ORNL designed and constructed a new version of their vision-based sensing system better adapted to acquire process signals of the TPC induction welding process for process anomaly and defect detection. In BP2, the team accomplished key tasks & milestones to scale up multi-source ML for TPC aerostructure consolidation and assembly from the lab-coupon scale to the pilot-industrial scale. In BP2, the team demonstrated real time anomaly & defect detection via experiments performed by ORNL & RTRC. The team completed ML-optimization heating trials for TPC induction consolidation at Collins, and the team confirmed pilot industrial scale experimental data from Collins was compatible with the developed ML pipeline from RTRC. The team completed sub-element scale ML process optimization demonstration at RTRC, where the team leveraged RTRC’s robotic TPC welding setup to de-risk the ML process optimization by performing ML analysis of recorded temperatures to account for complex part features. Then, the team applied its ML-derived control strategies and ML process optimization framework at Collins to the pilot-industrial scale on a demo skin-stiffener part representative of a nacelle aerostructure fan cowl section. The key innovation is the AI/ML framework enabling effective process development of high performance, lightweight, energy efficient TPCs for composite aircraft structures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Intercomparison of Three Continuous Monitoring Systems on Operating Oil and Gas Sites

We compare continuous monitoring systems (CMS) from three different vendors on six operating oil and gas sites in the Appalachian Basin using several months of data. We highlight similarities and differences between the three CMS solutions when deployed in the field and compare their output to concurrent top-down aerial measurements and to site-level bottom-up inventories. Furthermore, we compare vendor-provided emission rate estimates to estimates from an open-source quantification algorithm applied to the raw CMS concentration data. This experimental setup allows us to separate the effect of the sensor platform (i.e., sensor type and arrangement) from the quantification algorithm. We find that 1) localization and quantification estimates rarely agree between the three CMS solutions on short time scales (i.e., 30 min), but temporally aggregated emission rate distributions are similar between solutions, 2) differences in emission rate distributions are generally driven by the quantification algorithm, rather than the sensor platform, 3) agreement between CMS and aerial rate estimates varies by CMS solution but is close to parity when CMS estimates are averaged across solutions, and 4) similar sites with similar bottom-up inventories do not necessarily have similar emission characteristics. These results have important implications for developing measurement-informed inventories and for incorporating CMS-inferred emission characteristics into emission mitigation efforts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Autonomous Discovery in Science and Engineering

The Center for Advanced Mathematics for Energy Research Applications (CAMERA) is an integrated, cross-disciplinary center aimed at inventing, developing, and delivering the fundamental new mathematics required to capitalize on experimental investigations at scientific facilities. Jointly funded by the Office of Advanced Scientific Computing Research (ASCR) and the Office of Basic Energy Sciences (BES) within the US Department of Energy’s Office of Science, CAMERA identifies areas in experimental science that can be aided by new mathematical insights, develops the needed algorithmic tools, and delivers them as user-friendly software to the experimental community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Phasing of seven-channel fibre laser radiation with dynamic turbulent phase distortions using a stochastic parallel gradient algorithm at a bandwidth of 450 kHz

We have demonstrated an experimental setup for the coherent phasing of a seven-channel fibre laser system ( λ = 1064 nm) in a scheme comprising a master oscillator and a set of parallel amplifiers with lithium niobate-based fibre-optic phase modulators. Using a stochastic parallel gradient algorithm, an instrumental phase modulator control unit ensures a bandwidth of the system up to 450 kHz. The effectiveness of phasing of light transmitted through a turbulent medium with a characteristic time scale τ{sub turb} has been studied experimentally as a function of phasing time τ{sub ph}. The results demonstrate that the average Strehl ratio begins to rise at τ{sub turb}/τ{sub ph} ⩾ 2 and that the effectiveness of compensation for dynamic phase distortions in the beam propagation path rises sharply at τ{sub turb}/τ{sub ph} ≈ 20. For τ{sub turb}/τ{sub ph} ⩾ 30 – 40, the average Strehl ratio remains constant at the level reached. (control of laser radiation parameters)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Autonomous Closed-Loop Experimental Characterization and Dynamic Model Validation of a Scaled Underwater Kite

This paper presents the closed-loop experimental framework and dynamic model validation for a 1/12-scale underwater kite design. The pool-based tow testing framework described herein, which involves a fully actuated, closed-loop controlled kite and flexible tether, significantly expands upon the capabilities of any previously developed open-source framework for experimental underwater kite characterization. Specifically, the framework has allowed for the validation of three closed-loop flight control strategies, along with a critical comparison between dynamic model predictions and experimental results. In this paper, we provide a detailed presentation of the experimental tow system and kite setup, describe the control algorithms implemented and tested, and quantify the level of agreement between our multi-degree-of-freedom kite dynamic model and experimental data. Finally, we also present a sensitivity analysis that helps to identify the most influential parameters to kite performance and further explain the remaining mismatches between the model and data.

42 ENGINEERING↗
DOE OSTI2022

PyApprox: Enabling efficient model analysis

PyApprox is a Python-based one-stop-shop for probabilistic analysis of scientific numerical models. Easy to use and extendable tools are provided for constructing surrogates, sensitivity analysis, Bayesian inference, experimental design, and forward uncertainty quantification. The algorithms implemented represent the most popular methods for model analysis developed over the past two decades, including recent advances in multi-fidelity approaches that use multiple model discretizations and/or simplified physics to significantly reduce the computational cost of various types of analyses. Simple interfaces are provided for the most commonly-used algorithms to limit a user’s need to tune the various hyper-parameters of each algorithm. However, more advanced work flows that require customization of hyper-parameters is also supported. An extensive set of Benchmarks from the literature is also provided to facilitate the easy comparison of different algorithms for a wide range of model analyses. This paper introduces PyApprox and its various features, and presents results demonstrating the utility of PyApprox on a benchmark problem modeling the advection of a tracer in ground water.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Parallel Randomized Tucker Decomposition Algorithms

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. Here, we propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two algorithms that scale to large data and many processors, significantly reduce both computation and communication cost compared to previous deterministic and randomized approaches, and obtain nearly the same approximation errors. The key idea in our algorithms is to perform randomized sketches with Kronecker-structured random matrices, which reduces computation compared to unstructured matrices and can be implemented using a fundamental tensor computational kernel. We provide probabilistic error analysis of our algorithms and implement a new parallel algorithm for the structured randomized sketch. Our experimental results demonstrate that our combination of randomization and parallelization achieves accurate Tucker decompositions much faster than alternative approaches. We observe up to a 16X speedup over the fastest deterministic parallel implementation on 3D simulation data.

Tucker decompositions↗
DOE OSTI2023

PyApprox: A software package for sensitivity analysis, Bayesian inference, optimal experimental design, and multi-fidelity uncertainty quantification and surrogate modeling

PyApprox is a Python-based one-stop-shop for probabilistic analysis of numerical models such as those used in the earth, environmental and engineering sciences. Easy to use and extendable tools are provided for constructing surrogates, sensitivity analysis, Bayesian inference, experimental design, and forward uncertainty quantification. The algorithms implemented represent a wide range of methods for model analysis developed over the past two decades, including recent advances in multi-fidelity approaches that use multiple model discretizations and/or simplified physics to significantly reduce the computational cost of various types of analyses. An extensive set of Benchmarks from the literature is also provided to facilitate the easy comparison of new or existing algorithms for a wide range of model analyses. Here, this paper introduces PyApprox and its various features, and presents results demonstrating the utility of PyApprox on a benchmark problem modeling the advection of a tracer in groundwater.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Robust implementation of generative modeling with parametrized quantum circuits

Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansätze, a robust and thorough assessment on-hardware of such features has been missing to date. From the optimizer perspective, the primary challenge lies in the solver’s stochastic nature, and their significant variance over the random initialization. Therefore, a robust comparison requires one to perform several training curves for each solver before one can reach conclusions about their typical performance. Since each of the training curves requires the execution of thousands of quantum circuits in the quantum computer, such a robust study remained a steep challenge for most hybrid platforms available today. In this work, we leverage on Rigetti’s Quantum Cloud Services (QCS™) to overcome this implementation barrier, and we study the on-hardware performance of the data-driven quantum circuit learning (DDQCL) for three different state-of-the-art classical solvers, and on two-different circuit ansätze associated to different entangling connectivity graphs for the same task. Additionally, we assess the gains in performance from varying circuit depths. To evaluate the typical performance associated with each of these settings in this benchmark study, we use at least five independent runs of DDQCL towards the generation of quantum generative models capable of capturing the patterns of the canonical Bars and Stripes dataset. In this experimental benchmarking, the gradient-free optimization algorithms show an outstanding performance compared to the gradient-based solver. In particular, one of them had better performance when handling the unavoidable noisy objective function to be minimized under experimental conditions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Ultrafast radiographic imaging and tracking: An overview of instruments, methods, data, and applications

Ultrafast radiographic imaging and tracking (U-RadIT) use state-of-the-art ionizing particle and light sources to experimentally study sub-nanosecond transients or dynamic processes in physics, chemistry, biology, geology, materials science and other fields. These processes are fundamental to modern technologies and applications, such as nuclear fusion energy, advanced manufacturing, communication, and green transportation, which often involve one mole or more atoms and elementary particles, and thus are challenging to compute by using the first principles of quantum physics or other forward models. One of the central problems in U-RadIT is to optimize information yield through, e.g. high-luminosity X-ray and particle sources, efficient imaging and tracking detectors, novel methods to collect data, and large-bandwidth online and offline data processing, regulated by the underlying physics, statistics, and computing power. We review and highlight recent progress in: (a.) Detectors such as high-speed complementary metal-oxide semiconductor (CMOS) cameras, hybrid pixelated array detectors integrated with Timepix4 and other application-specific integrated circuits (ASICs), and digital photon detectors; (b.) U-RadIT modalities such as dynamic phase contrast imaging, dynamic diffractive imaging, and four-dimensional (4D) particle tracking; (c.) U-RadIT data and algorithms such as neural networks and machine learning, and (d.) Applications in ultrafast dynamic material science using XFELs, synchrotrons and laser-driven sources. Hardware-centric approaches to U-RadIT optimization are constrained by detector material properties, low signal-to-noise ratio, high cost and long development cycles of critical hardware components such as ASICs. Interpretation of experimental data, including comparisons with forward models, is frequently hindered by sparse measurements, model and measurement uncertainties, and noise. Alternatively, U-RadIT make increasing use of data science and machine learning algorithms, including experimental implementations of compressed sensing. Machine learning and artificial intelligence approaches, refined by physics and materials information, may also contribute significantly to data interpretation, uncertainty quantification and U-RadIT optimization.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Neural architecture search via similarity adaptive guidance

Evolutionary neural network architecture search (ENAS) has attracted the attention of many experts due to its global optimization capabilities to automatically search for convolutional neural network architectures based on the target task. The current search space for ENAS is not to design a fully structured network, but to search for smaller cell architectures to reduce search costs. However, blind search strategies do not effectively utilize the potential experience of the population. In order to utilize the potential experience learned by the current population to guide the evolutionary search of the population, we propose a similarity guided neural network architecture search algorithm based on cell architecture, which utilizes the similarity between pairwise architectures in the population as empirical knowledge learned by the population. Our proposed algorithm provides a novel method for calculating architecture similarity, which calculates architecture similarity separately from the cell and macro-structure. Then we decouple the connections and operations in the cell and calculate connection and operation similarity separately. In addition, we propose adaptive similarity selection and binary tournament selection strategies to enhance the algorithm’s global and local search capabilities and effectively explore the search space. Finally, we design an improved single-point crossover operator to enhance the local search ability of the evolutionary operator. The experimental results show that SAGNAS is a competitive algorithm that achieves 97.44% and 81.60% in CIFAR10 and CIFAR100 with only 1.9 GPU-days spent.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Retrieving Top-k Hyperedge Triplets: Models and Applications

Complex systems frequently exhibit multi-way, rather than pairwise, interactions. These group interactions can- not be faithfully modeled as collections of pairwise interactions using graphs and instead require hypergraphs. However, methods that analyze hypergraphs directly, rather than via lossy graph reductions, remain limited. Hypergraph motifs hold promise in this regard, as motif patterns serve as building blocks for larger group interactions which are inexpressible by graphs. Recent work has focused on categorizing and counting hypergraph motifs based on the existence of nodes in hyperedge intersection regions. Here, we argue that the relative sizes of hyperedge inter- sections within motifs contain varied and valuable information. We propose a suite of efficient algorithms for finding top-k triplets of hyperedges based on optimizing the sizes of these intersection patterns. This formulation uncovers interesting local patterns of interaction, finding hyperedge triplets that either (1) are the least similar with each other, (2) have the highest pairwise but not groupwise correlation, or (3) are the most similar with each other. We formalize this as a combinatorial optimization problem and design efficient algorithms based on filtering hyperedges. Our comprehensive experimental evaluation shows that the resulting hyperedge triplets yield insightful information on real-world hypergraphs. Our approach is also orders of magnitude faster than a naive baseline implementation.

hypergraphs, motifs, Combinatorial Algorithms↗
DOE OSTI2023

Machine learning assisted phase and size-controlled synthesis of iron oxide particles

Synthesis of iron oxides with specific phases and particle sizes is a crucial challenge in various fields, including materials science, energy storage, biomedical applications, environmental science, and earth science. However, despite significant advances in this area, much of the current palette of particle outcomes has been based on time-consuming trial-and-error exploration of synthesis conditions. The present study was designed to explore a very different approach to 1) predict the outcome of synthesis from specified reaction parameters based on using machine learning (ML) techniques, and 2) correlate sets of parameters to obtain products with desired outcomes by a newly designed recommendation algorithm. To achieve this, four ML algorithms were tested, namely random forest, logistic regression, support vector machine, and k-nearest neighbor. Among the models, random forest outperformed the others, attaining 96% and 81% accuracy when predicting the phase and size of iron oxide particles in the test dataset. Surprisingly, the permutation feature importance analysis revealed that volume, which may strongly relate to pressure, was one of the important features, along with precursor concentration, pH, temperature, and time, influencing the phase and size of iron oxide particles during synthesis. To verify the robustness of the random forest models, prediction and experimental results were compared based on 24 randomly generated methods in additive and non-additive systems not included in the datasets. The predictions of product phase and particle size from the models agreed well with the experimental results. Furthermore, a searching and ranking algorithm was developed to recommend potential synthesis parameters for obtaining iron oxide products with the desired phase and particle size from previous studies in the dataset. Furthermore, this study lays the foundation for a closed-loop approach in materials synthesis and preparation, beginning with suggesting potential reaction parameters from the dataset and predicting potential outcomes, followed by conducting experiments and analyses, and ultimately enriching the dataset.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Chemistry on Quantum Computers with Virtual Quantum Subspace Expansion

Several novel methods for performing calculations relevant to quantum chemistry on quantum computers have been proposed but not yet explored experimentally. Virtual quantum subspace expansion is one such algorithm developed for modeling complex molecules using their full orbital space and without the need for additional quantum resources. Here, we implement this method on the IBM Q platform and calculate the potential energy curves of the hydrogen and lithium dimers using only two qubits and simple classical post-processing. A comparable level of accuracy would require twenty qubits with previous approaches. We also develop an approach to minimize the impact of experimental noise on the stability of a generalized eigenvalue problem that is a crucial component of the algorithm. Our results demonstrate that virtual quantum subspace expansion works well in practice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗