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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials using MALAMUTE

The Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy aims to develop and qualify additively manufactured materials for nuclear applications. One key challenge to this is the microstructural variability observed in the additively manufactured products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-throughput experimental and modeling techniques to accelerate qualification. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the additive manufacturing process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture microstructural variability is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning models to develop a digital twin for additive manufacturing that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation. The melting and subsequent solidification that occurs during the additive process is a complex phenomenon that requires multiscale multiphysics analysis. This work package focuses on understanding the role of process variabilities on the unique microstructural characteristics of additively manufactured materials. Microstructural features at the subgrain level, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. Idaho National Laboratory’s Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for additively manufactured materials in an efficient, reliable, and cost-effective way. This work focuses on capturing the microstructural variabilities at the subgrain level that are often missing in the part-scale models. In fiscal year 2025, we significantly advanced upon our work in the last fiscal year, in terms of the predictive capabilities of the physics-based and ML models, by adding the capabilities to capture subgrain-level micro-segregation during solidification using phase-field model and to predict the time-dependent dynamics of the AM process through the MOGPAR model. The alloy solidification model in MOOSE incorporates the thermodynamic properties and free energy relevant to 316 stainless steel. The model demonstrates the Cr and Ni segregation that occurs during solidification, including that the rate of solidification. The microstructural evolution model is connected to the process conditions via the surrogate model developed in this work. This enables predictions of the final microstructure in conjunctions with the manufacturing process. This work supports AMMT's rapid qualification goals by laying the foundation for an efficient and cost-effective model establishing the PSPP correlation for AM. The generated microstructures and predicted micro-segregation can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work helps to identify the key microstructural features at the subgrain level that are significant in property and performance predictions of additively manufactured components. This work will also provide inputs to the large-scale process variability models to reevaluate and validate assumptions and simplifications made in the part-scale models. Furthermore, through active learning this work can help identify the data need from both modeling and experimental sides for development of a robust digital twin for additive manufacturing and accelerate the AMMT's qualification efforts.

36 - MATERIALS SCIENCE↗
DOE OSTI2020

Deep machine learning-assisted multiphoton microscopy to reduce light exposure and expedite imaging

Two-photon excitation fluorescence (2PEF) allows imaging of tissue up to about one millimeter in thickness. Typically, reducing fluorescence excitation exposure reduces the quality of the image. However, using deep learning super resolution techniques, these low-resolution images can be converted to high-resolution images. This work explores improving human tissue imaging by applying deep learning to maximize image quality while reducing fluorescence excitation exposure. We analyze two methods: a method based on U-Net, and a patch-based regression method. Both methods are evaluated on a skin dataset and an eye dataset. The eye dataset includes 1200 paired high power and low power images of retinal organoids. The skin dataset contains multiple frames of each sample of human skin. High-resolution images were formed by averaging 70 frames for each sample and low-resolution images were formed by averaging the first 7 and 15 frames for each sample. The skin dataset includes 550 images for each of the resolution levels. We track two measures of performance for the two methods: mean squared error (MSE) and structural similarity index measure (SSIM). For the eye dataset, the patches method achieves an average MSE of 27,611 compared to 146,855 for the U-Net method, and an average SSIM of 0.636 compared to 0.607 for the U-Net method. For the skin dataset, the patches method achieves an average MSE of 3.768 compared to 4.032 for the U-Net method, and an average SSIM of 0.824 compared to 0.783 for the U-Net method. Despite better performance on image quality, the patches method is worse than the U-Net method when comparing the speed of prediction, taking 303 seconds to predict one image compared to less than one second for the U-Net method.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Multiscale and Machine Learning Modeling for Process-informed Microstructure Prediction in Additively Manufactured Materials Using MALAMUTE

Advanced Materials and Manufacturing Technologies (AMMT) program under the Department of Energy Office of Nuclear Energy, aims to develop and qualify additively-manufactured materials for nuclear applications. The key challenges to these efforts are the microstructural variabilities observed on the AM products and their impact on the properties and performance of the material in extreme environments. AMMT is using a combination of high-through-put experimental and modeling techniques to accelerate the qualification efforts. Conventionally, in-situ and ex-situ characterizations and testing are performed to correlate different aspects of the AM process to the final product and its performance. However, adopting a trial-and-error approach to experimentally evaluate the vast range of process parameters required to capture the microstructural variabilities is cost-prohibitive. Modeling and simulation provide a comparatively inexpensive way to understand and correlate the microstructural evolution to the processing conditions. The modeling and simulation work-packages within the AMMT program aims to use physics-based and machine learning modeling capabilities to develop a digital twin for AM that can correlate the process conditions to the final product and establish a process-structure-property-performance (PSPP) correlation for AM materials. The melting and subsequent solidification that occurs during the AM process is a complex phenomenon that requires multiscale multiphysics analysis. Idaho National Laboratory’s (INL) Multiphysics Object-Oriented Simulation Environment (MOOSE), specifically the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) software, provides an ideal platform for developing the multiphysics multiscale model to explore the intricacies of the microstructural evolution during the AM processes within a single framework. Furthermore, given that such full-fidelity simulations can be computationally intensive, reduced order models are necessary to explore the PSPP space for AM materials in an efficient, reliable, and cost-effective way. This work package focuses on understanding the role of process variabilities on the various microstructural characteristics of the AM materials. Microstructures unique to AM materials, such as compositional micro-heterogeneity and dislocation cells, are of particular interest here since they can influence the creep properties and radiation performance. In fiscal year (FY) 24, we significantly advanced upon our work in the last fiscal year, both on physics-based and ML models. The alloy solidification model available in MOOSE has been extended to incorporate the thermodynamic properties and free energy relevant to 316SS. The model demonstrates the Cr segregation that occurs during solidifcation. It is demonstrated that rate of solidification and solute segregation is primarily influence by the cooling rate dictating the level of freezing. This work captures the microstructural variabilities at the subgrain level that are often missing in the part-scale models. With an aim to connect the microstructural evolution model to realistic process conditions, a reduced order model is developed for predicting the thermal conditions around meltpool from high-fidelity process simulations. Furthermore, machine learning approach is used to accelerate the temperature prediction during the AM process. In the following years, MALAMUTE will be used to connect different aspects of the models and quantitatively predict the microstructural evolution. The developed ML-based surrogate model will consider the process conditions as the input to predict the microstructural features in a cost-effective way. The generated microstructures can be used by other work packages under AMMT to evaluate the properties and environmental response of the material at the mesoscale. Thus, this work help identify the key microstructural features at the subgrain level that are significant in property/performance prediction of the AM products. This work will provide inputs to the large-scale process variability models to reevaluate and validate assumptions/simplifications made in the part-scale models. Furthermore, through active learning this work will help identify the data need from both modeling and experimental sides for development of a robust digital twin for AM.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Error-controlled Progressive Retrieval of Scientific Data under Derivable Quantities of Interest

The unprecedented amount of scientific data has introduced heavy pressure on the current data storage and transmission systems. Progressive compression has been proposed to mitigate this problem, which offers data access with on-demand precision. However, existing approaches only consider precision control on primary data, leaving uncertainties on the quantities of interest (QoIs) derived from it. In this work, we present a progressive data retrieval framework with guaranteed error control on derivable QoIs. Our contributions are three-fold. (1) We carefully derive the theories to strictly control QoI errors during progressive retrieval. Our theory is generic and can be applied to any QoIs that can be composited by the basis of derivable QoIs proved in the paper. (2) We design and develop a generic progressive retrieval framework based on the proposed theories, and optimize it by exploring feasible progressive representations. (3) We evaluate our framework using five real-world datasets with a diverse set of QoIs. Experiments demonstrate that our framework can faithfully respect any user-specified QoI error bounds in the evaluated applications. This leads to over 2.02× performance gain in data transfer tasks compared to transferring the primary data while guaranteeing a QoI error that is less than 1E-5.

Wu, Xuan↗
DOE OSTI2025

Exponentially Reduced Circuit Depths Using Trotter Error Mitigation

Product formulas are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance, which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by the use of these formulas. This work provides a rigorous, general analysis of these techniques for computing time-evolved observables, simplifying the interpolation algorithm in the process, and shows that extrapolation generically improves the performance of product formulas for this task. We demonstrate that, to achieve error 𝜖 in a simulation of time 𝑇 using a 𝑝 ⁢th-order product formula with extrapolation, circuit depths of 𝑂⁡(𝑇 1+1/𝑝 ⁢polylog (1/𝜖)) are sufficient—an exponential improvement in the precision over product formulas alone. Furthermore, we prove that these algorithms achieve commutator scaling, and improve the 𝑇 complexity for the interpolation algorithm. By relaxing the requirement of performing exact Chebyshev interpolation, our simplified algorithm eliminates the need for fractional implementations of Trotter steps, reducing computational overhead. Finally, we show these techniques can be combined with the classical shadows method to estimate many time-evolved local observables. Taken together, our findings provide the strongest evidence yet for the utility of Trotter error-mitigation techniques in algorithmic applications.

quantum algorithms & computation↗
DOE OSTI2020

Error-mitigated data-driven circuit learning on noisy quantum hardware

Application-level benchmarks measure how well a quantum device performs meaningful calculations. In the case of parameterized circuit training, the computational task is the preparation of a target quantum state via optimization over a loss landscape. This is complicated by various sources of noise, fixed hardware connectivity, and generative modeling, the choice of target distribution. Gradient-based training has become a useful benchmarking task for noisy intermediate-scale quantum computers because of the additional requirement that the optimization step uses the quantum device to estimate the loss function gradient. In this work, we use gradient-based data-driven circuit learning to qualitatively evaluate the performance of several superconducting platform devices and present results that show how error mitigation can improve the training of quantum circuit Born machines with 28 tunable parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Machine learning based unfolding of x-ray spectra from filter stack spectrometer data

We demonstrate the application of neural networks to perform x-ray spectra unfolding from data collected by filter stack spectrometers. A filter stack spectrometer consists of a series of filter-detector pairs, where the detectors behind each filter measure the energy deposition through each layer as photo-stimulated luminescence (PSL). The network is trained on synthetic data, assuming x-rays of energies < 1 MeV and of two different distribution functions (Maxwellian and Gaussian) and the corresponding measured PSL values obtained from five different filter stack spectrometer designs. Predicted unfolds of single distributions are near identical reproductions of the ground truth spectra, with differences in the values lower than 20% at the higher energy end in some cases. The neural network has also demonstrated robustness to experimental measurement errors of < 5% and some capability of performing unfolds for linear combinations of the two distributions without previous training. The network can perform unfolds at rates > 1 Hz, ideal for application to some high-repetition-rate systems.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Analysis and prediction of intersection traffic violations using automated enforcement system data

We report that the automated enforcement system (AES) is an effective way of supplementing traditional traffic enforcement, and the traffic violation data from AES can also be effectively used for safety research. In this study, traffic violation data were used to analyze the influencing factors associated with traffic violations and to predict the probability of violations at intersections. The potential factors influencing violations include 24 independent factors related to time, space, traffic and weather. Results from a logistic model showed that the midday period, weekends, residential districts, collector roads, congested traffic conditions, high traffic flow, lower wind speed and low temperature would increase the probability of traffic violations. The probability of violations was predicted by the random forest algorithm, which was proven to be the best traffic violation prediction model among logistic regression, Gaussian naive Bayes, and support vector machine. Moreover, the proximity weighted synthetic oversampling technique (ProWSyn) method was applied to reduce the impact of the imbalance ratio (IR) and improve the model’s prediction performance. The receiver operating characteristics (ROC) curves and Precision-Recall (PR) curves illustrated that the random forest algorithm using oversampling data had the best classifier prediction performance than undersampling data. The area under curve (AUC) and out-of-bag (OOB) error with IR = 1 reached 0.914 and 0.0787, which showed the better performance of the random forest algorithm using ProWSyn in dealing with imbalanced traffic violation data.

42 ENGINEERING↗
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 OSTI2022

Behavior and mechanisms of Doppler wind lidar error in varying stability regimes

Abstract. Wind lidars are widespread and important tools in atmospheric observations. An intrinsic part of lidar measurement error is due to atmospheric variability in the remote-sensing scan volume. This study describes and quantifies the distribution of measurement error due to turbulence in varying atmospheric stability. While the lidar error model is general, we demonstrate the approach using large ensembles of virtual WindCube V2 lidar performing a profiling Doppler-beam-swinging scan in quasi-stationary large-eddy simulations (LESs) of convective and stable boundary layers. Error trends vary with the stability regime, time averaging of results, and observation height. A systematic analysis of the observation error explains dominant mechanisms and supports the findings of the empirical results. Treating the error under a random variable framework allows for informed predictions about the effect of different configurations or conditions on lidar performance. Convective conditions are most prone to large errors (up to 1.5 m s−1 in 1 Hz wind speed in strong convection), driven by the large vertical velocity variances in convective conditions and the high elevation angle of the scanning beams (62∘). Range-gate weighting induces a negative bias into the horizontal wind speeds near the surface shear layer (−0.2 m s−1 in the stable test case). Errors in the horizontal wind speed and direction computed from the wind components are sensitive to the background wind speed but have negligible dependence on the relative orientation of the instrument. Especially during low winds and in the presence of large errors in the horizontal velocity estimates, the reported wind speed is subject to a systematic positive bias (up to 0.4 m s−1 in 1 Hz measurements in strong convection). Vector time-averaged measurements can improve the behavior of the error distributions (reducing the 10 min wind speed error standard deviation to <0.3 m s−1 and the bias to <0.1 m s−1 in strong convection) with a predictable effectiveness related to the number of decorrelated samples in the time window. Hybrid schemes weighting the 10 min scalar- and vector-averaged lidar measurements are shown to be effective at reducing the wind speed biases compared to cup measurements in most of the simulated conditions, with time averages longer than 10 min recommended for best use in some unstable conditions. The approach in decomposing the error mechanisms with the help of the LES flow field could be extended to more complex measurement scenarios and scans.

17 WIND ENERGY↗
DOE OSTI2024

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

B-spline↗
DOE OSTI2025

Comparing Machine Learning and Physics-Based Nanoparticle Geometry Determinations Using Far-Field Spectral Properties

Anisotropic metal nanostructures exhibit polarization-dependent light scattering, a property which has been widely studied and exploited to determine orientations of subwavelength structures using far-field microscopy. Here we explore the use of variational autoencoders (VAEs) to determine the geometries of gold nanorods (NRs) such as in-plane orientation and aspect ratio under linearly polarized dark-field illumination in an optical microscope. We enforce a shared latent space to connect two VAEs trained separately with polarized dark-field scattering spectra and electron microscopy images and achieve image prediction (shape, orientation, and size) of Au NRs using only polarized dark-field scattering spectra. We determine the geometrical parameters of orientational angle and aspect ratio quantitatively via both our dual-VAE and physics-based analysis on the input scattering spectra. We show that orientational angle prediction by dual-VAE performs well with only a small (~300 particle) training set, yielding a mean absolute error (MAE) of 14.4° and a concordance correlation coefficient (CCC) of 0.95. This performance is only marginally worse than the physics-based cos(2?) fitting approach between the scattering intensity and the polarizing angle, which achieves MAE of 8.78° and CCC of 0.99. Aspect ratio determination is also comparable for the dual-VAE and physics-based fitting comparison (MAE of 0.21 vs. 0.23 and CCC of 0.53 vs. 0.68). Here, this dual encoder-decoder architecture effectively exploits the structure-property relationships of plasmonic nanostructures to construct a cross-modal machine learning (ML) approach, providing a pathway to employ ML approaches to address other structure-property relationships in materials science.

Dark-field scattering↗
DOE OSTI2026

Resilience of the surface code to error bursts

Quantum error correction works effectively only if the error rate of gate operations is sufficiently low. However, some rare physical mechanisms can cause a temporary increase in the error rate that affects many qubits; examples include ionizing radiation in superconducting hardware and large deviations in the global control of atomic systems. We refer to such rare transient spikes in the gate error rate as error bursts. In this work, we investigate the resilience of the rotated surface code to generic error bursts. We assume that, after appropriate mitigation strategies, the spike in the error rate lasts for only a single syndrome-extraction cycle; we also assume that the enhanced error rate is uniform across the code block. Under these assumptions, and for a circuit-level depolarizing noise model, we perform Monte Carlo simulations to determine the regime in burst error rate and background error rate for which the memory time becomes arbitrarily long as the code block size grows. Our results indicate that suitable hardware mitigation methods combined with standard decoding methods may suffice to protect against transient error bursts in the rotated surface code.

Quantum error correction↗
DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Combined Computer Vision and Deep Learning Approach for Rapid Drone-Based Optical Characterization of Parabolic Troughs

Optical accuracy is a primary driver of parabolic trough concentrating solar power (CSP) plant performance, but can be damaged by wind loads, gravity, error during installation, and regular plant operation. Collecting and analyzing optical measurements over an entire operating parabolic trough plant is difficult, given the large scale of typical installations. Distant Observer, a software tool developed at the National Renewable Energy Laboratory, uses images of the absorber tube reflected in the collector mirror to measure both surface slope in the parabolic mirror and offset of the absorber tube from the ideal focal point. This technology has been adapted for fast data collection using low-cost commercial drones, but until recently still required substantial human labor to process large amounts of data. A new method leveraging advanced deep learning and computer vision tools can drastically reduce the time required to process images. This new method addresses the primary analysis bottleneck, identifying featureless, reflective mirror corner points to a high degree of accuracy. Recent work has shown promising results using computer vision methods. The combined deep learning and computer vision approach presented here proved highly effective and has the potential to further automate data collection and analysis, making the tool more robust. The method presented in this paper automatically identified 74.3% of mirror corners within 2 pixels of their manually marked counterparts and 91.9% within 3 pixels. This level of accuracy is sufficient for practical Distant Observer analysis within a target uncertainty. A commercial drone collected video of over 100 parabolic trough modules at an operating CSP plant to demonstrate the deep learning and computer vision method's usefulness in processing large amounts of data. These troughs were successfully analyzed using Distant Observer, paired with the new deep learning and computer vision algorithm, and can provide plant operators and trough designers with valuable insight about plant performance, operating strategies, and plant-wide optical error trends.

computer vision↗
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 OSTI2021

Antiferromagnetic character of the quantum phase transition in the Hubbard model on the honeycomb lattice

In this work we provide a unified, comprehensive treatment of all operators that contribute to the antiferromagnetic, ferromagnetic, and charge-density-wave structure factors and order parameters of the hexagonal Hubbard Model. We use the Hybrid Monte Carlo algorithm to perform a systematic, carefully controlled analysis in the temporal Trotter error and of the thermodynamic limit. We expect our findings to improve the consistency of Monte Carlo determinations of critical exponents. We perform a data collapse analysis and determine the critical exponent β = 0.898 (37) for the semimetal-Mott insulator transition in the hexagonal Hubbard Model. Our methods are applicable to a wide range of lattice theories of strongly correlated electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Dual-map framework for noise characterization of quantum computers

In order to understand the capabilities and limitations of quantum computers, it is necessary to develop methods that efficiently characterize and benchmark error channels present on these devices. In this paper, we present a method that faithfully reconstructs a marginal (local) approximation of the effective noise (MATEN) channel, that acts as a single layer at the end of the circuit. We first introduce a dual-map framework that allows us to analytically derive expectation values of observables with respect to noisy circuits. These findings are supported by numerical simulations of the quantum approximate optimization algorithm (QAOA) that also justify the MATEN, even in the presence of nonlocal errors that occur during a circuit. Finally, we demonstrate the performance of the method on Rigetti's Aspen-11 quantum computer for QAOA circuits up to six qubits, successfully predicting the observed measurements on a majority of the qubits.

Sud, James↗