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At least 163 records · Page 9

On Rank Selection for Nonnegative Matrix Factorization

Rank selection, i.e. the choice of factorization rank, is the first step in constructing Nonnegative Matrix Factorization (NMF) models. It is a long-standing problem which is not unique to NMF, but arises in most models which attempt to decompose data into its underlying components. Since these models are often used in the unsupervised setting, the rank selection problem is further complicated by the lack of ground truth labels. In this paper, we review and empirically evaluate the most commonly used schemes for NMF rank selection.

Eswar, Srinivas [Argonne National Laboratory]↗

FTTN: Feature-Targeted Testing for Numerical Properties of NVIDIA & AMD Matrix Accelerators

While NVIDIA has been the dominant provider of GPUs for HPC and ML, now AMD has several offerings of GPUs. This encourages programmers to try out AMD GPUs for new codes and also port existing codes over. Unfortunately, without understanding the floating-point differences between these GPU types, software development or porting can introduce bugs—and currently such an understanding is lacking. The magnitude of this open question becomes clear if one imagines the the number of floating-point precision choices (FP16, FP32, etc.), floating-point formats (standard floats, brain-float, etc.), and execution units available (elementary units, matrix/tensor cores, etc.) Questions such as rounding modes and subnormal support are also important. Most of these answers are unknown today or are hard to access. We provide the first testing-guided approach that answers a significant number of these questions. We also devise tests to reveal internal information (e.g., extra bits kept) to make sure that our findings are reliable. Many of our tests employ systematically generated random-programs, others apply fast-math flags and some involve fused multiplyadd. Especially for tensor/matrix cores, the tests have nontrivial logic that we present Our testing approach is reusable for the plethora of GPUs yet to be introduced. Our findings include up to 7 ulps of difference between NVIDIA and AMD for sin and cos at FP32 precision and 3 ulp at FP64. In our study of matrix cores (NVIDIA) and tensor cores (AMD), we have extensively characterized rounding modes (truncation versus round-to-nearest), the number of extra internal bits kept (whether 3 bits are kept or not), subnormal support for inputs and outputs across four different floating-point formats and across NVIDIA A100 and AMD MI250X GPUs. We believe that this wealth of data becoming available for the first time may help avoid significant porting bugs when migrating code across these platforms.

Li, Xinyi↗

A Novel Low-Profile High-Efficiency Three-Phase Matrix Transformer

High step-down isolated DC-DC conversion from an 800 V DC bus to low-voltage, high-current outputs is required in automotive auxiliary converters and data center power supplies. In such applications, conventional transformer-based converters require large turns ratios, which increase winding resistance, leakage inductance, and magnetic height. This paper proposes a novel low-profile three-phase matrix transformer that realizes a large effective voltage ratio through flux division among multiple secondary legs, without increasing the physical turns count of each winding. As a result, the proposed structure reduces copper usage and transformer height while preserving the voltage conversion capability of a conventional three-phase transformer. Finite element analysis shows that the proposed design reduces magnetic height by 27%, ferrite volume by 34%, and copper volume by 28%. Circuit-level simulations of an 800 V/12 V,3 kW CLLLC dual-active-bridge converter further show that the lower winding resistance reduces total system loss by 91% and increases DC-DC efficiency from 82.6% to 97.6% at 3 kW output.

Inoue, Shuntaro [ORNL] (ORCID:0000000262637627)↗

On the Stability of Power Transmission Systems Under Persistent Inverter Attacks: A Bi-Linear Matrix Approach

We investigate the stability and robustness properties of a power transmission system under persistent deceiving attacks on inverter-interfaced energy resources. The attacks can corrupt the damping coefficients in the inverters' controllers and measurements of the frequency at the points of coupling. Leveraging tools from hybrid dynamical systems theory, we characterize a broad family of persistent (and not necessarily periodic) attacks acting on the inverters, under which the stability properties of the transmission system can be shown to not be compromised. To address potentially conservative conditions identified through conventional bounding techniques, sufficient conditions on the average activation time of the attacks are identified via Lyapunov theory, as well as the formulation and solution of a class of bilinear matrix inequalities (BMI). The results are obtained for constant and slowly time-varying loads via input-to-state stability (ISS) tools. Numerical simulations on the IEEE 39-bus test system are also presented.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Algorithms for Non-Negative Matrix Factorization on Noisy Data With Negative Values

Non-negative matrix factorization (NMF) is a dimensionality reduction technique that has shown promise for analyzing noisy data, especially astronomical data. For these datasets, the observed data may contain negative values due to noise even when the true underlying physical signal is strictly positive. Prior NMF work has not treated negative data in a statistically consistent manner, which becomes problematic for low signal-to-noise data with many negative values. In this paper we present two algorithms, Shift-NMF and Nearly-NMF, that can handle both the noisiness of the input data and also any introduced negativity. Both of these algorithms use the negative data space without clipping or masking and recover non-negative signals without any introduced positive offset that occurs when clipping or masking negative data. We demonstrate this numerically on both simple and more realistic examples, and prove that both algorithms have monotonically decreasing update rules.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Posterior Covariance Matrix Approximations

Here, the Davis equation of state (EOS) is commonly used to model thermodynamic relationships for high explosive (HE) reactants. Typically, the parameters in the EOS are calibrated, with uncertainty, using a Bayesian framework and Markov Chain Monte Carlo (MCMC) methods. However, MCMC methods are computationally expensive, especially for complex models with many parameters. This paper provides a comparison between MCMC and less computationally expensive Variational methods (Variational Bayesian and Hessian Variational Bayesian) for computing the posterior distribution and approximating the posterior covariance matrix based on heterogeneous experimental data. All three methods recover similar posterior distributions and posterior covariance matrices. This study demonstrates that for this EOS parameter calibration application, the assumptions made in the two Variational methods significantly reduce the computational cost but do not substantially change the results compared to MCMC.

97 MATHEMATICS AND COMPUTING↗

Environmental matrix and moisture influence soil microbial phenotypes in a simplified porous media incubation

Soil moisture and porosity regulate microbial metabolism by influencing factors, such as system chemistry, substrate availability, and soil connectivity. However, accurately representing the soil environment and establishing a tractable microbial community that limits confounding variables is difficult. Here, we use a reduced-complexity microbial consortium grown in a glass bead porous media amended with chitin to test the effects of moisture and a structural matrix on microbial phenotypes. Leveraging metagenomes, metatranscriptomes, metaproteomes, and metabolomes, we saw that our porous media system significantly altered microbial phenotypes compared with the liquid incubations, denoting the importance of incorporating pores and surfaces for understanding microbial phenotypes in soils. These phenotypic shifts were mainly driven by differences in expression of Streptomyces and Ensifer, which included a significant decrease in overall chitin degradation between porous media and liquid. Our findings suggest that the success of Ensifer in porous media is likely related to its ability to repurpose carbon via the glyoxylate shunt amidst a lack of chitin degradation byproducts while potentially using polyhydroxyalkanoate granules as a C source. We also identified traits expressed by Ensifer and others, including motility, stress resistance, and carbon conservation, that likely influence the metabolic profiles observed across treatments. Together, these results demonstrate that porous media incubations promote structure-induced microbial phenotypes and are likely a better proxy for soil conditions than liquid culture systems. Furthermore, they emphasize that microbial phenotypes encompass not only the multi-enzyme pathways involved in metabolism but also include the complex interactions with the environment and other community members.

54 ENVIRONMENTAL SCIENCES↗

A Study of Performance Portability of Low-bit Fused Matrix-Vector Multiplication Kernels in SYCL

Understanding the causes of performance gaps between a portable programming model and a vendor-specific programming model is important for improving performance portability. This paper studies performance portability of low-bit fused general matrix-vector multiplication kernels in SYCL on vendors’ graphics processing units (GPUs). This work introduces the use case, explains the kernel implementations in detail, evaluates the performance of the CUDA, HIP, and SYCL kernels on datacenter, desktop, and laptop GPUs, and investigates the causes of performance gaps. The results show that loop unrolling, kernel dispatch overhead, and sum reduction contribute to the gaps.

Jin, Zheming [ORNL] (ORCID:000000027197780X)↗

Matrix-based Omnidirectional Pressure Integratio

This software enables the calculation of the pressure field based on experimental velocity measurements utilizing the matrix-based omnidirectional pressure integration algorithm developed by Dr. John Charonko and Dr. Fernando Zigunov, which is several orders of magnitude faster than the current state of the art.

Zigunov, Fernando↗

Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation

Low-rank methods have shown success in accelerating simulations of a collisionless plasma described by the Vlasov equation, but still rely on computationally costly linear algebra every time step. We propose a data-driven factorization method using artificial neural networks, specifically with convolutional layer architecture, that trains on existing simulation data. At inference time, the model outputs a low-rank decomposition of the distribution field of the charged particles, and we demonstrate that this step is faster than the standard linear algebra technique. Numerical experiments show that the method achieves comparable reconstruction accuracy for interpolation tasks, generalizing to unseen test data in a manner beyond just memorizing training data; patterns in factorization also inherently followed the same numerical trend as those within algebraic methods (e.g., truncated singular-value decomposition). However, when training on the first 70% of a time-series data and testing on the remaining 30%, the method fails to meaningfully extrapolate. Despite this limiting result, the technique may have benefits for simulations in a statistical steady-state or otherwise showing temporal stability. These results suggest that while the model offers a computationally efficient alternative for datasets with temporal stability, its current formulation is best suited for interpolation rather than for predicting future states in time-evolving systems. This study thus lays the groundwork for further refinement of neural network-based approaches to low-rank matrix factorization in high-dimensional plasma simulations.

97 MATHEMATICS AND COMPUTING↗

Density-matrix mean-field theory

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Physics↗

Innovations in Direct Air Capture: Unveiling a Simple and Robust Synthesized Fibrous Amine-functionalized Matrix (FAM) Sorbent for Commercial Scale-up

The escalating challenge of climate change necessitates innovative solutions in the realm of carbon management, particularly in mitigating the impact of fossil fuel emissions. Direct Air Capture (DAC) technology emerged as a critical component within the spectrum of Carbon Capture and Sequestration (CCS) solutions, offering the distinct advantage of directly removing CO2 from the atmosphere irrespective of the source. This attribute grants DAC systems unparalleled flexibility in deployment locations and the potential to make substantial contributions to lowing atmospheric CO2 levels. The success of DAC technologies significantly depends on the development of an efficient, economical sorbent capable of selective and durable CO2 capture from ambient air. Recent advancements in material science have led to the exploration of amine-functionalized sorbents, hollow fiber sorbents and membranes, and other novel materials designed to meet these criteria. This study explores a novel Fibrous Amine-functionalized Matrix (FAM) sorbent. The FAM sorbent distinguished itself through its mechanical robustness, a streamlined synthesis process, and the capability for low-temperature regeneration (is 90 oC really low temperature?). FAM’s exceptional adsorption-desorption kinetics enable swift CO2 capture and release, crucial for the viability of DAC on a commercial scale. The synthesis process involves a simple dip-coating technique, allowing crosslinked amines to coat glass substrates.

Wang, Qiuming↗

Impact of Source Geometry on Detector Response Matrix Efficiency: Simulations of the PFUNS-MUSiC Experiments

This work looks at two different bare highly enriched uranium (HEU) systems, configuration one from Measurements of Uranium Subcritical and Critical (MUSiC) and Prompt Fission Uranium Neutron Spectrum (PFUNS) to see the effect geometry has on detector efficiency and the response matrix. The distance from the multiplying source, the medium between the source and detector, and the geometry of the source all play a part in the efficiency of the detector. These factors are especially important when performing spectrum unfolding. Spectrum unfolding is a process used to reconstruct a true spectrum from measured detector response data. It involves interpreting a set of measured values, such as a light signal from a scintillator, to recover the original neutron energy spectrum. This leads to the question, how much will the efficiency of a detector change when you measure a point source compared to an extended source? The distance and solid angle from the source to the detector may be different. It may only be a minuscule change, but in the spectrum unfolding process it can have a considerable effect on the unfolded spectrum

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Indirect reactions and connection with R-matrix theory

It is often the case that nuclear reactions that are important for societal applications or basic science are difficult to measure directly in existing facilities for accelerated beams. The difficulty might be associated with an exceedingly small cross section, as the ones obtained at beam energies well below the Coulomb barrier, or with the impossibility of devising a short-lived target, as is the case for neutron-induced reactions on unstable isotopes. The fruitful line of experimental research addressing this issue with alternative (indirect) reactions has been developed in parallel to the theory needed to make the connection between the observed data and the desired cross sections of the (direct) reaction under study. Within this context, we present here an explicit connection between the indirect cross section and the R-matrix parameters which describe the energy-dependent cross section of the desired direct reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

New Matrix Framework to Determine Carbon Storage Technical Viability

Carbon storage is an integral component of reducing CO2 emissions. Research over the past two decades has developed workflows for volume assessments and economic project feasibility, providing necessary and useful tools to progress geologic carbon storage (GCS) projects. These workflows and assessments have focused primarily on determining the in-situ storage resource based on geologic and engineering parameters and do not integrate subsurface characterization with surface conditions, social factors, and environmental factors that may pose a benefit or impediment to the implementation of GCS. Furthermore, the data required to assess the technical viability of GCS are myriad and disparate. There is no current methodology that identifies technical viability criteria and systematically informs how to aggregate these factors for spatial assessments. To address this gap, the National Energy Technology Laboratory has developed a Carbon Storage Technical Viability Approach (CS TVA) Matrix that incorporates a wide variety of factors to inform and accelerate screening for GCS site selection in the United States.

Mulhern, Julia↗

Phase-Field Modeling of Mechanical Damages in Ceramic Matrix Composites

Developed a phase-field model for mechanical damages in CMCs, which incorporates the CMC microstructures, matrix cracking, fiber breakage, and interfacial sliding. Two types of mechanisms, fiber bridging and fiber pull-out, are considered. The obtained simulation results agree with experimental observations and an analytical solution. Simulation results suggest that the performance of CMCs would be enhanced with thicker fibers, longer fibers, and higher fiber density. Opposite trends of interfacial sliding resistances are suggested for the two types of situations. In reality, a mixture of the two situations may exist, and then an intermediate interfacial sliding resistance may be optimal.

Xue, Fei↗

Advanced Measurements for Resilient Integration of Inverter-Based Resources: PROGRESS MATRIX Final Report

As nearly every aspect of the electric power grid undergoes rapid change, measurement technologies that support grid operation and planning must evolve as well. The rapid large-scale deployment of inverter-based resources (IBRs) vital to achieving the nation’s clean energy goals has in some cases led to negative impacts on the reliability and security of the bulk power system (BPS). Advanced power system measurements, including synchronized phasor and waveform measurements, are key to making IBR integration secure and reliable. To this end, the Department of Energy (DOE) initiated the PROGRESS MATRIX project to develop advanced measurement capabilities and analytics that will accelerate adoption of IBRs while improving the reliability and resilience of the BPS. This report discusses the outcomes of the project, which was a joint effort between the Pacific Northwest National Laboratory (PNNL), Oak Ridge National Laboratory (ORNL), the National Renewable Energy Laboratory (NREL), and Lawrence Berkeley National Laboratory (LBNL). In the project’s first year, PNNL, NREL, and ORNL partnered with the Bonneville Power Administration (BPA), the Western Area Power Administration (WAPA), and Kauai Island Utility Cooperative (KIUC) to understand their existing measurement capabilities and the gaps limiting deployment of IBR-focused measurement systems and analytics. The other primary activity in the first year was deployment of GridSweep instruments, which provide unprecedented precision in waveform measurement while probing distribution systems. The instruments were deployed at Dominion Energy and the University of California, Riverside. In the project’s second year, the input from partner utilities and collected measurements were used to advance measurement capabilities. Twelve analytical methods spanning disturbance analysis, power plant evaluation, feeder evaluation, and modeling were developed. Two software tools were developed, one to analyze GridSweep measurements and another to automatically evaluate the control performance of power plants connected to the BPS. Testbeds at ORNL and NREL were augmented to better enable studies of IBR integration. The project culminated in demonstrations of these analytical methods, software tools, and testbeds, both in the field and in the laboratory. This report discusses these various accomplishments and documents the significant progress in developing advanced measurement capabilities to support the secure, reliable, and accelerated adoption of IBRs in the BPS.

24 POWER TRANSMISSION AND DISTRIBUTION↗