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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Hardware-Efficient Quantum Phase Estimation via Local Control

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

Schiffer, Benjamin F. [Max Planck Institute of Qua↗
DOE OSTI2017

Bayesian calibration of terrestrial ecosystem models: a study of advanced Markov chain Monte Carlo methods

Calibration of terrestrial ecosystem models is important but challenging. Bayesian inference implemented by Markov chain Monte Carlo (MCMC) sampling provides a comprehensive framework to estimate model parameters and associated uncertainties using their posterior distributions. The effectiveness and efficiency of the method strongly depend on the MCMC algorithm used. In this work, a differential evolution adaptive Metropolis (DREAM) algorithm is used to estimate posterior distributions of 21 parameters for the data assimilation linked ecosystem carbon (DALEC) model using 14 years of daily net ecosystem exchange data collected at the Harvard Forest Environmental Measurement Site eddy-flux tower. The calibration of DREAM results in a better model fit and predictive performance compared to the popular adaptive Metropolis (AM) scheme. Moreover, DREAM indicates that two parameters controlling autumn phenology have multiple modes in their posterior distributions while AM only identifies one mode. The application suggests that DREAM is very suitable to calibrate complex terrestrial ecosystem models, where the uncertain parameter size is usually large and existence of local optima is always a concern. In addition, this effort justifies the assumptions of the error model used in Bayesian calibration according to the residual analysis. Here, the result indicates that a heteroscedastic, correlated, Gaussian error model is appropriate for the problem, and the consequent constructed likelihood function can alleviate the underestimation of parameter uncertainty that is usually caused by using uncorrelated error models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Effect of Time Window and Spectral Measurement Options on Empirical Green’s Function Analysis Using DAS Array and Seismic Stations

The recorded seismic waveform is a convolution of event source term, path term, and station term. Removing high-frequency attenuation due to path effect is a challenging problem. Empirical Green’s function (EGF) method uses nearly collocated small earthquakes to correct the path and station terms for larger events recorded at the same station. However, this method is subject to variability due to many factors. Here, we focus on three events that were well recorded by the seismic network and a rapid response distributed acoustic sensing (DAS) array. Using a suite of high-quality EGF events, we assess the influence of time window, spectral measurement options, and types of data on the spectral ratio and relative source time function (RSTF) results. Increased number of tapers (from 2 to 16) tends to increase the measured corner frequency and reduce the source complexity. Extended long time window (e.g., 30 s) tends to produce larger variability of corner frequency. The multitaper algorithm that simultaneously optimizes both target and EGF spectra produces the most stable corner-frequency measurements. The stacked spectral ratio and RSTF from the DAS array are more stable than two nearby seismic stations, and are comparable to stacked results from the seismic network, suggesting that DAS array has strong potential in source characterization.

58 GEOSCIENCES↗
DOE OSTI2023

How reliable is distribution of relaxation times (DRT) analysis? A dual regression-classification perspective on DRT estimation, interpretation, and accuracy

The distribution of relaxation times (DRT) has gained increasing attention and adoption in recent years as a versatile method for analyzing electrochemical impedance spectroscopy (EIS) data obtained from complex devices like fuel cells, electrolyzers, and batteries. The DRT deconvolutes the impedance without a priori specification of a generative model, which is especially useful for interpretation and model selection when the governing principles of the system under study are not fully understood. However, DRT estimation is an ill-posed inversion problem that must be addressed with a subjective choice of regularization and tuning, which leaves substantial risk of misleading interpretations of EIS data. In this work, we suggest a new classification view of the DRT inversion to clarify DRT estimation and interpretation. We introduce a dual regression-classification framework that unifies the classification and regression views of the DRT inversion with wide-reaching implications for DRT analysis. The dual framework is employed to demonstrate a new kind of DRT inversion algorithm and develop novel evaluation metrics that capture previously ignored aspects of DRT accuracy. These approaches are applied to both synthetic data and experimental spectra collected from a protonic ceramic fuel cell and a lithium-ion battery to illustrate their broad utility. The dual inversion algorithm shows promising performance for accurate DRT estimation and autonomous model identification, while the dual evaluation approach produces metrics that meaningfully assess the strengths and risks of DRT algorithms. Here this work provides valuable insight for both practical application of the DRT to experimental data and further development of EIS analysis methods.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Performance Enhancement of APW+lo Calculations by Simplest Separation of Concerns

Full-potential linearized augmented plane wave (LAPW) and APW plus local orbital (APW+lo) codes differ widely in both their user interfaces and in capabilities for calculations and analysis beyond their common central task of all-electron solution of the Kohn–Sham equations. However, that common central task opens a possible route to performance enhancement, namely to offload the basic LAPW/APW+lo algorithms to a library optimized purely for that purpose. To explore that opportunity, we have interfaced the Exciting-Plus (“EP”) LAPW/APW+lo DFT code with the highly optimized SIRIUS multi-functional DFT package. This simplest realization of the separation of concerns approach yields substantial performance over the base EP code via additional task parallelism without significant change in the EP source code or user interface. We provide benchmarks of the interfaced code against the original EP using small bulk systems, and demonstrate performance on a spin-crossover molecule and magnetic molecule that are of size and complexity at the margins of the capability of the EP code itself.

Zhang, Long↗
DOE OSTI2024

Periodicity significance testing with null-signal templates: reassessment of PTF’s SMBH binary candidates

Periodograms are widely employed for identifying periodicity in time series data, yet they often struggle to accurately quantify the statistical significance of detected periodic signals when the data complexity precludes reliable simulations. We develop a data-driven approach to address this challenge by introducing a null-signal template (NST). The NST is created by carefully randomizing the period of each cycle in the periodogram template, rendering it non-periodic. It has the same frequentist properties as a periodic signal template, and we show with simulations that the distribution of false positives is the same as with the original periodic template, regardless of the underlying data. Thus, performing a periodicity search with the NST acts as an effective simulation of the null (no-signal) hypothesis, without having to simulate the noise properties of the data. We apply the NST method to the supermassive black hole binaries (SMBHB) search in the Palomar Transient Factory (PTF), where Charisi et al. had previously proposed 33 high signal-to-noise candidates utilizing simulations to quantify their significance. Our approach reveals that these simulations do not capture the complexity of the real data. There are no statistically significant periodic signal detections above the non-periodic background. To improve the search sensitivity, we introduce a Gaussian quadrature based algorithm for the Bayes Factor with correlated noise as a test statistic. We show with simulations that this improves sensitivity to true signals by more than an order of magnitude. However, the Bayes Factor approach also results in no statistically significant detections in the PTF data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Survey of Surveys: I. The largest compilation of radial velocities for the Galaxy

In the present-day panorama of large spectroscopic surveys, the amount, diversity, and complexity of the available data continuously increase. The overarching goal of studying the formation and evolution of our Galaxy is hampered by the heterogeneity of instruments, selection functions, analysis methods, and measured quantities. Here, we present a comprehensive catalogue, the Survey of Surveys (SoS), built by homogeneously merging the radial velocity (RV) determinations of the largest ground-based spectroscopic surveys to date, such as APOGEE, GALAH, Gaia-ESO, RAVE, and LAMOST, using Gaia as a reference. This pilot study serves to prove the concept and to test the methodology that we plan to apply in the future to the stellar parameters and abundance ratios as well. We have devised a multi-staged procedure that includes: (i) the cross match between Gaia and the spectroscopic surveys using the official Gaia cross-match algorithm, (ii) the normalisation of uncertainties using repeated measurements or the three-cornered hat method, (iii) the cross calibration of the RVs as a function of the main parameters on which depend (magnitude, effective temperature, surface gravity, metallicity, and signal-to-noise ratio) to remove trends and zero point offsets, and (iv) the comparison with external high-resolution samples, such as the Gaia RV standards and the Geneva-Copenhagen survey, to validate the homogenisation procedure and to calibrate the RV zero-point of the SoS catalogue. We provide the largest homogenised RV catalogue to date, containing almost 11 million stars, of which about half come exclusively from Gaia and half in combination with the ground-based surveys. We estimate the accuracy of the RV zero-point to be about 0.16–0.31 km s –1 and the RV precision to be in the range 0.05–1.50 km s –1 depending on the type of star and on its survey provenance. We validate the SoS RVs with open clusters from a high resolution homogeneous samples and provide the systemic velocity of 55 individual open clusters. Additionally, we provide median RVs for 532 clusters recently discovered by Gaia data. The SoS is publicly available and ready to be applied to various research projects, such as the study of star clusters, Galactic archaeology, stellar streams, or the characterisation of planet-hosting stars, to name a few. We also plan to include survey updates and more data sources in future versions of the SoS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Failure prediction using machine learning in a virtualised HPC system and application

Failure is an increasingly important issue in high performance computing and cloud systems. As large-scale systems continue to grow in scale and complexity, mitigating the impact of failure and providing accurate predictions with sufficient lead time remains a challenging research problem. Traditional existing fault-tolerance strategies such as regular check-pointing and replication are not adequate because of the emerging complexities of high performance computing systems. This necessitates the importance of having an effective as well as proactive failure management approach in place aimed at minimizing the effect of failure within the system. With the advent of machine learning techniques, the ability to learn from past information to predict future pattern of behaviours makes it possible to predict potential system failure more accurately. Thus, in this paper, we explore the predictive abilities of machine learning by applying a number of algorithms to improve the accuracy of failure prediction. We have developed a failure prediction model using time series and machine learning, and performed comparison based tests on the prediction accuracy. The primary algorithms we considered are the support vector machine (SVM), random forest (RF), k-nearest neighbors (KNN), classification and regression trees (CART) and linear discriminant analysis (LDA). Experimental results indicates that the average prediction accuracy of our model using SVM when predicting failure is 90% accurate and effective compared to other algorithms. This finding implies that our method can effectively predict all possible future system and application failures within the system.

Mohammed, Bashir↗
DOE OSTI2025

Minimal cyclic behavior in sheared amorphous solids

Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle rearrangements are represented by interacting spin flips called hysterons, capture many features of this periodic behavior. Yet it has been unclear to what extent individual rearrangements can be described by such binary objects and how such objects interact with one another. Using a particularly sensitive algorithm, we identify rearrangements in simulated jammed packings and select pairs of rearrangements that undo one another to create periodic cyclic behavior. We find that the rearrangement pairs surprisingly persist down to the smallest increments in strain, even in the smallest systems we can study. We explore the statistics of these rearrangement pairs and find that there is a relation between the amount of hysteresis and the energy drop and mean-square displacement of the particles; these results are inconsistent with the scaling found in models that treat rearrangements as localized buckling events. Finally, our analysis shows that there is no clean distinction between the particle motions that represent the identity of a single, individual rearrangement and the particle motions that lead to interactions between separated rearrangements or hysterons. These results offer insight into how complex systems such as amorphous solids can reach a limit cycle.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Inferring microbial interactions with their environment from genomic and metagenomic data

Microbial communities assemble through a complex set of interactions between microbes and their environment, and the resulting metabolic impact on the host ecosystem can be profound. Microbial activity is known to impact human health, plant growth, water quality, and soil carbon storage which has lead to the development of many approaches and products meant to manipulate the microbiome. In order to understand, predict, and improve microbial community engineering, genome-scale modeling techniques have been developed to translate genomic data into inferred microbial dynamics. However, these techniques rely heavily on simulation to draw conclusions which may vary with unknown parameters or initial conditions, rather than more robust qualitative analysis. To better understand microbial community dynamics using genome-scale modeling, we provide a tool to investigate the network of interactions between microbes and environmental metabolites over time. Using our previously developed algorithm for simulating microbial communities from genome-scale metabolic models (GSMs), we infer the set of microbe-metabolite interactions within a microbial community in a particular environment. Because these interactions depend on the available environmental metabolites, we refer to the networks that we infer as metabolically contextualized , and so name our tool MetConSIN: Met abolically Con textualized S pecies I nteraction N etworks.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Enhancing Cluster Identification in Atom Probe Tomography Data Using Transfer Learning

Atom Probe Tomography (APT) is a powerful technique for visualizing the atomic-scale distribution of solutes in materials, but quantitative cluster analysis of APT datasets remains a challenge due to the need for subjective parameter selection in clustering algorithms. While distance-based and density-based methods such as HDBSCAN are widely used, their performance is highly sensitive to user-defined parameters, which undermines reproducibility and accuracy. This study proposes an image-based, deep learning-aided workflow for automating parameter selection and cluster detection in APT data analysis. By projecting 3D APT point clouds onto 2D planes, we leverage pretrained convolutional neural networks (ConvNeXt-Tiny and ResNet-50) through transfer learning to predict the number of clusters present in synthetic datasets. The output is used to guide K-means clustering and estimate HDBSCAN parameters, specifically minimum cluster size and minimum sample points. This approach reduces reliance on manual parameter tuning, improving consistency and scalability. The methodology demonstrates the feasibility of using image-based deep learning for interpreting complex spatial patterns in APT data, enabling faster and more objective analysis. The complete workflow and code are made publicly available to support reproducibility and future research.

Density-based clustering↗
DOE OSTI2025

2025 Advances in NekRS: Supporting improved performance for nuclear applications

This report presents several 2025 advancements in NekRS, a high-fidelity spectral element CFD code developed at Argonne National Laboratory to support the NEAMS thermal-hydraulics program. The forthcoming v25 release consolidates several of these advances, adding new features for portability across heterogeneous GPU architectures, real-time in situ visualization, improved turbulence modeling, and conjugate heat transfer coupling. Over the past year, NekRS has demonstrated strong scalability and performance on DOE’s leading exascale platforms, including Aurora and Frontier, confirming its readiness for some of the largest and most complex simulations attempted to date. These achievements provide a powerful new platform for high-fidelity data generation, which in turn supports the development and validation of advanced closure models critical for reactor safety and design. Significant algorithmic innovations have also been introduced. A new global runtime h-refinement capability simplifies workflows by reducing mesh preparation burdens and enabling coarse-to-fine restarts. Building on this, a novel multigrid strategy was implemented to accelerate pressure and transport solves at scale, addressing long-standing bottlenecks in exascale CFD. Together, these developments improve both the efficiency and accessibility of high-fidelity simulations for reactor-relevant problems. Collectively, these enhancements represent a major step forward in simulation technology, positioning NekRS as a cornerstone of NEAMS efforts to enable accurate, efficient, and scalable high-fidelity analysis of advanced nuclear systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Winners are not keepers: Characterizing household engagement, gains, and energy patterns in demand response using machine learning in the United States

Demand-response programs can help utilities manage rapidly evolving electric grids, but these programs are subject to the complexities of human behavior. This paper explores a novel method for uncovering heterogeneity in households. In this work, we use a machine-learning method known as a Conditional Inference Tree (c-tree) algorithm to categorize households based on their energy behavior characteristics collected via smart meters, and explore how this translates through into heterogeneity in their real-world response to a DR program. Using data from randomized controlled trial, we generate estimates of the changes in energy use caused by the program within each household group. Our results show that the c-tree approach differentiates households by their energy-use characteristics in a way that increases the spread in enrollment rates and critical peak reduction among household groups, compared with the spreads achieved via several conventional segmentation methods. Thus, the c-tree analysis enables the most tailored targeting of major potential energy savers and could provide the greatest increase in cost-effectiveness of household recruitment into DR programs. Our results also offer fresh insights into the relationships between household energy behavior characteristics – such as peak energy use and “structural winningness” (the ability to save money under a DR program without changing energy-use behaviors) – and household decisions about enrolling in DR programs and reducing energy use. Our research also demonstrates the potential of smart meter data, combined with machine learning and econometric methods, to provide significant value to utilities, program implementers, researchers, and other stakeholders.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Identification of drug repurposing candidates for amyotrophic lateral sclerosis using electronic health records: a retrospective cohort study

Amyotrophic lateral sclerosis (ALS) is a progressive neurodegenerative disease with a life expectancy of only 3–5 years and few approved treatments. To identify drug repurposing candidates for the treatment of ALS, we analysed the electronic health records (EHRs) of a large cohort of military veterans with ALS. We analysed the EHRs of individuals in the US Veterans Health Administration (VHA) database who were diagnosed with ALS between Jan 1, 2009 and Dec 31, 2019 to assess medication effects. Individuals without recorded prescriptions after the date of diagnosis were excluded. Two sets of criteria were applied to ascertain exposure. Exposure criteria A were met if the dispense date or the end date of the medication was within 12 months of ALS diagnosis and the end date was at least 6 months after the dispense date. Exposure criteria B were met if there were at least two dispenses within 6 months before diagnosis and 12 months after diagnosis. Propensity score-matched control groups were generated on the basis of confounders included in the EHR, with methodology of potential outcomes used to infer treatment effects. The primary outcome was death. A standard Cox proportional hazards analysis was done to assess association with survival. Survival was defined as the time from diagnosis date recorded in the EHR to death reported in the Department for Veterans Affairs Vital Status File. Follow-up survival time was censored on Dec 31, 2020, for those alive on this date. Downstream protein targets of drugs with clinically significant effects were analysed using the protein–protein interaction networks-based algorithm PathFX. The EHRs of 11 003 individuals with ALS in the VHA database were appropriate for analysis. 162 medications with treatment groups of 30 or more individuals were identified. Among these 162 medications, 27 were associated with statistically significant changes (≥0·1) in the hazard ratio (HR) for death. 18 of the medications were associated with a reduced HR for death (prolonged survival), and nine were associated with an increased HR for death (reduced survival). Drugs associated with reduced HR included HMG-CoA reductase inhibitors (simvastatin, pravastatin, lovastatin, and atorvastatin), PDE5 inhibitors (vardenafil and sildenafil), and α-adrenergic antagonists (tamsulosin and terazosin). The medications associated with an increased HR were drugs used either in the management of clinical features of ALS associated with poor outcomes or in end-of-life care. PathFx analysis identified a complex of proteins interacting with several of the identified drugs. To our knowledge, this analysis is the largest EHR-based study for identifying drug repurposing candidates for ALS. We identified several drugs that warrant further assessment as therapeutic options in ALS, as well as a protein network complex that might serve as a therapeutic target for ALS.

Reimer, Richard J. [Stanford Univ., CA (United Sta↗
DOE OSTI2018

Evaluation and Comparison of Machine Learning Techniques for Rapid QSTS Simulations

Rapid and accurate quasi-static time series (QSTS) analysis is becoming increasingly important for distribution system analysis as the complexity of the distribution system intensifies with the addition of new types, and quantities, of distributed energy resources (DER). The expanding need for hosting capacity analysis, control systems analysis, photovoltaic (PV) and DER impact analysis, and maintenance cost estimations are just a few reasons that QSTS is necessary. Historically, QSTS analysis has been prohibitively slow due to the number of computations required for a full-year analysis. Therefore, new techniques are required that allow QSTS analysis to rapidly be performed for many different use cases. This research demonstrates a novel approach to doing rapid QSTS analysis for analyzing the number of voltage regulator tap changes in a distribution system with PV components. A representative portion of a yearlong dataset is selected and QSTS analysis is performed to determine the number of tap changes, and this is used as training data for a machine learning algorithm. The machine learning algorithm is then used to predict the number of tap changes in the remaining portion of the year not analyzed directly with QSTS. The predictions from the machine learning algorithms are combined with the results of the partial year simulation for a final prediction for the entire year, with the goal of maintaining an error <10% on the full-year prediction. Five different machine learning techniques were evaluated and compared with each other; a neural network ensemble, a random forest decision tree ensemble, a boosted decision tree ensemble, support vector machines, and a convolutional neural network deep learning technique. A combination of the neural network ensemble together with the random forest produced the best results. Using 20% of the year as training data, analyzed with QSTS, the average performance of the technique resulted in ~2.5% error in the yearly tap changes, while maintaining a <10% 99.9 th percentile error bound on the results. This is a 5x speedup compared to a standard, full-length QSTS simulation. These results demonstrate the potential for applying machine learning techniques to facilitate modern distribution system analysis and further integration of distributed energy resources into the power grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Nearly Optimal Lattice Simulation by Product Formulas

We consider simulating an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t on a quantum computer. We show that this simulation has gate complexity (nt)1+o(1) using product formulas, a straightforward approach that has been demonstrated by several experimental groups. While it is reasonable to expect this complexity—in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill—we are not aware of a straightforward proof. Furthermore, our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Optimal net-load balancing in smart grids with high PV penetration

Mitigating mismatches in supply demand curve is critical for smooth power grid operation. Traditionally, load curtailment techniques such as Demand Response (DR) have been used for this purpose. However, smart grids with high PV penetration sometimes exhibit supply surplus causing over-voltages. Thus, load curtailment techniques cannot be the only component of a net-load balancing framework. Supply curtailment techniques such as Volt-Var Optimizations are complex and computationally expensive. This increases the complexity of net-load balancing systems used by the grid operator and limits their scalability. Recently, new technologies have been developed that enable the rapid and selective connection of PV modules of an installation to the grid. Taking advantage of these advancements, we develop a unified optimal net-load balancing framework which performs both load and solar curtailment. We show that when the available curtailment values are discrete, this problem is NP-hard and develop bounded approximation algorithms for minimizing the curtailment cost. Our algorithms produce fast solutions, given the tight timing constraints required for grid operation. We also incorporate the notion of fairness to ensure that curtailment is evenly distributed among all the nodes. Finally, we develop an online algorithm which performs net-load balancing using only data available for the current interval. Using both theoretical analysis and practical evaluations, we show that our net-load balancing algorithms provide solutions which are close to optimal in a small amount of time.

14 SOLAR ENERGY↗
DOE OSTI2018

Algorithmic Patterns for $$\mathcal {H}$$-Matrices on Many-Core Processors

In this work, we consider the reformulation of hierarchical ( \(\mathcal {H}\) ) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). \(\mathcal {H}\) matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix–vector products. The parallelization of \(\mathcal {H}\) matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing \(\mathcal {H}\) matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full \(\mathcal {H}\) matrix construction and the fast matrix–vector product to many-core hardware. In this work, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source \(\mathcal {H}\) matrix library of this kind. We investigate application examples as present in kernel ridge regression, Gaussian Process Regression and kernel-based interpolation. In this context, an in-depth performance analysis and a comparative performance study against a standard multi-core CPU \(\mathcal {H}\) matrix library highlights profound speedups of our many-core parallel approach.

97 MATHEMATICS AND COMPUTING↗