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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 sources NASA NTRS DOE OSTI

DOE OSTI2024

A Provably Accurate Randomized Sampling Algorithm for Logistic Regression

In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we present a simple, randomized sampling-based algorithm for logistic regression problem that guarantees high-quality approximations to both the estimated probabilities and the overall discrepancy of the model. Our analysis builds upon two simple structural conditions that boil down to randomized matrix multiplication, a fundamental and well-understood primitive of randomized numerical linear algebra. We analyze the properties of estimated probabilities of logistic regression when leverage scores are used to sample observations, and prove that accurate approximations can be achieved with a sample whose size is much smaller than the total number of observations. To further validate our theoretical findings, we conduct comprehensive empirical evaluations. Overall, our work sheds light on the potential of using randomized sampling approaches to efficiently approximate the estimated probabilities in logistic regression, offering a practical and computationally efficient solution for large-scale datasets.

Chowdhury, Agniva↗

DOE OSTI2021

Quantum Random Number Generator (QRNG)

The Los Alamos QRNG is a hardware-based high-performance Random Number Generator capable of generating 200 Mbit/s or more of true random numbers. The device harvests entropy from fluctuations in an optical source that arise from quantum mechanical properties of light. These quantum effects are irreducibly random; the resulting numbers are unpredictable and beyond the influence of any adversary. Qrypt, Inc., launched in 2017, has amassed multiple quantum entropy sources to create high-quality random keys at scale. The company is engaging with Los Alamos through license and a Cooperative Research and Development Agreement to facilitate the transition of QRNG technology and deploy the technology into the marketplace.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Random Circuits in the Black Hole Interior

In this paper, we present a quantitative holographic relation between a microscopic measure of randomness and the geometric length of the wormhole in the black hole interior. To this end, we perturb an AdS black hole with Brownian semiclassical sources, implementing the continuous version of a random quantum circuit for the black hole. We use the random circuit to prepare ensembles of states of the black hole whose semiclassical duals contain Einstein-Rosen (ER) caterpillars: long cylindrical wormholes with large numbers of matter inhomogeneities, of linearly growing length with the circuit time. In this setup, we show semiclassically that the ensemble of ER caterpillars of average length $k\ell_Δ$ and matter correlation scale $\ell_Δ$ forms an approximate quantum state $k$-design of the black hole. At exponentially long circuit times, the ensemble of ER caterpillars becomes polynomial-copy indistinguishable from a collection of random states of the black hole. We comment on the implications of these results for holographic circuit complexity and for the holographic description of the black hole interior.

FOS: Physical sciences↗

DOE OSTI2020

C-SAW: a framework for graph sampling and random walk on GPUs

Many applications require to learn, mine, analyze and visualize large-scale graphs. These graphs are often too large to be addressed efficiently using conventional graph processing technologies. Fortunately, recent research efforts find out graph sampling and random walk, which significantly reduce the size of original graphs, can benefit the tasks of learning, mining, analyzing and visualizing large graphs by capturing the desirable graph properties. This paper introduces C-SAW, the first framework that accelerates Sampling and Random Walk framework on GPUs. Particularly, C-SAW makes three contributions: First, our framework provides a generic API which allows users to implement a wide range of sampling and random walk algorithms with ease. Second, offloading this framework on GPU, we introduce warp-centric parallel selection, and two novel optimizations for collision migration. Third, towards supporting graphs that exceed the GPU memory capacity, we introduce efficient data transfer optimizations for out-of-memory and multi-GPU sampling, such as workload-aware scheduling and batched multi-instance sampling. Taken together, our framework constantly outperforms the state of the art projects in addition to the capability of supporting a wide range of sampling and random walk algorithms.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Programmable pseudo-random sequence generator for use with universal lidar and its associated method of operation

A pseudo-random sequence generator for use within a universal lidar system and its corresponding method of operation. The pseudo-random sequence generator uses synchronized shift registers that are in series Binary adders are provided. The signal output of each of the shift registers is tapped and directed to the binary adders. High-speed switches are provided between the shift registers and the binary adders. The switches are programmed to connect only two of the shift registers to the binary adders for each of the pseudo-random patterns being generated. The binary adders generate an output signal that is received by the first shift register. The signal propagates through all the shift registers to the last shift register. The last shift register outputs a pseudo-random sequence.

Datta, Shubhashish↗

DOE OSTI2023

Structured ground states of randomly interacting bosons

Bosonic degrees of freedom and their emergence as part of complex quantum many-body dynamics, symmetries, collective behavior, clustering, and phase transitions play an important role in modern studies of quantum systems. In this paper, we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. Here, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal ϵ -2 asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Efficient light-trapping in ultrathin GaAs solar cells using quasi-random photonic crystals

Ultrathin solar cells reduce material usage and allow the use of lower-quality materials thanks to their one order of magnitude smaller thickness than their conventional counterparts. However, efficient photonic light-trapping is required to harvest the incident light efficiently for an otherwise insufficient absorber thickness. Quasi-random photonic crystals are predicted to have high efficient light-trapping while being more robust under angle and thickness variations than simple photonic crystals. In this study, we experimentally demonstrate a light-trapping solution based on quasi-random photonic crystals fabricated by polymer blend lithography. We control the average lattice parameter by modifying the spin-coating speed. We demonstrate an ultrathin GaAs cell of 260 nm with a rear quasi-random pattern with submicron features, and a J sc = 26.4 mA/cm 2 and an efficiency of 22.35% under the global solar spectrum.

14 SOLAR ENERGY↗

DOE OSTI2026

Negative fluxes and cell-miss errors in the random ray method

The random ray method is a recently developed stochastic method for solving neutral particle transport problems based on the method of characteristics. Perhaps surprisingly for a characteristics-based method using flat sources, we note that the random ray method can produce negative fluxes which may be numerically troublesome in several situations. These occur most severely in fixed source problems where the source is in a region with a small cross section. Additionally, we briefly discuss another source of bias which can occur in similar situations, namely a ray missing a mesh with a strong source and small cross section, resulting in the entirety of the source being unphysically deposited locally. This paper describes the mechanism by which negative fluxes may occur and several different methods to mitigate their effects. These fixes are tested on an eigenvalue problem, a ‘fusion-like’ shielding problem, and a shielding problem featuring an adjoint calculation. Even when extremely coarse random ray quadratures are used such that 20%–30% of cells are missed during a given iteration, use of the preferred fix technique ensures local flux tally errors remain trivial (below 1%). The preferred fix is now the default option in SCONE and OpenMC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

High-speed tunable generation of random number distributions using actuated perpendicular magnetic tunnel junctions

Perpendicular magnetic tunnel junctions (pMTJs) actuated by nanosecond pulses are emerging as promising devices for true random number generation (TRNG) due to their intrinsic stochastic behavior and high throughput. In this work, we demonstrate the tunability and quality of random number distributions generated by pMTJs operating at a frequency of 104 MHz. First, changing the pulse amplitude is used to systematically vary the probability bias. The variance of the resulting bitstreams closely matches the expected binomial distribution, demonstrating consistency with an underlying sequence of Bernoulli trials. Second, the quality of uniform distributions of 8-bit random numbers generated with a probability bias of 0.5 is considered. A reduced chi-square analysis of these data shows that only two XOR operations are sufficient to achieve this distribution with p-values greater than 0.05. Finally, we show that there is a correlation between long-term probability bias variations and pMTJ resistance. These findings suggest that variations in the characteristics of the pMTJ underlie the observed variation of probability bias. In conclusion, our results highlight the potential of stochastically actuated pMTJs for high-speed, tunable TRNG applications, showing the importance of the stability of pMTJ device characteristics in achieving reliable, long-term performance.

Magnetic tunnel junctions↗

DOE OSTI2025

Exact spectral gaps of random one-dimensional quantum circuits

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. Here, by focusing on the second moment of one-dimensional unitary circuits where nearest-neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Random magnetic field and the Dirac Fermi surface

In this paper, we study a single two-dimensional Dirac fermion at finite density, subject to a quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated to each point on the Fermi surface) coupled by a random vector potential. This low-energy theory exhibits an exactly solvable random fixed line, along which we directly compute various disorder-averaged observables without the need for the usual replica, supersymmetry, or Keldysh techniques. We find the longitudinal dc conductivity in the collisionless $\hbar$ω/k B T→∞ limit to be nonuniversal and to vary continuously along the fixed line.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Comparison of the spatial statistics of random and defined-sequence photoresist films

The resolution-line edge roughness-sensitivity tradeoff has motivated the exploration of potential improvements using defined sequence polymers and polymer-bound photoacid generators and quenchers. We characterize the internal structures of positive tone photoresist polymer films formed from defined sequence polymers and compare them with random copolymers of the same composition. We model their imaging to connect initially to developable film structures. We use a polymer packing algorithm to simulate films of diverse compositions and locations of photoacid generators and quenchers, using the composition of an ESCAP photoresist. We use a simple extreme ultraviolet exposure-deprotection algorithm to model developable image formation within them. In all cases, the spatial distribution of chemical moieties in the film for defined sequence polymers is nearly indistinguishable from random copolymers. We evaluate several exposure-deprotection scenarios and find that a defined sequence copolymer has a distinctive developable image under certain circumstances. The use of defined sequence polymers within a photoresist layer does not automatically result in improved imaging; however, they do have some characteristics different from random polymers of the same composition. Further study of these characteristics may provide a route to improved control over the nanoscale imaging process.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR with Column Pivoting (QRCP) is usually suitable for these purposes, but it can be much slower than the unpivoted QR algorithm. For large matrices, the difference in performance is due to increased communication between the processor and slow memory, which QRCP needs in order to choose pivots during decomposition. Our main algorithm, Randomized QR with Column Pivoting (RQRCP), uses randomized projection to make pivot decisions from a much smaller sample matrix, which we can construct to reside in a faster level of memory than the original matrix. This technique may be understood as trading vastly reduced communication for a controlled increase in uncertainty during the decision process. Furthermore, for rank-revealing purposes, the selection mechanism in RQRCP produces results that are the same quality as the standard algorithm, but with performance near that of unpivoted QR (often an order of magnitude faster for large matrices). Additionally, we also propose two formulas that facilitate further performance improvements. The first efficiently updates sample matrices to avoid computing new randomized projections. The second avoids large trailing updates during the decomposition in truncated low-rank approximations. Our truncated version of RQRCP also provides a key initial step in our truncated SVD approximation, TUXV. These advances open up a new performance domain for large matrix factorizations that will support efficient problem-solving techniques for challenging applications in science, engineering, and data analysis.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Randomized Algorithms for Symmetric Nonnegative Matrix Factorization

Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a matrix with a product of a nonnegative, low-rank matrix and it transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first method uses randomized matrix sketching to compute an initial low-rank approximation to the input matrix and proceeds to uses this as a low-rank input to rapidly compute a SymNMF. The second methods uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. Here, we prove theoretically that leverage score sampling can approximately solve constrained least squares problems to e-accuracy. Finally we demonstrate both methods work in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Estimating carrying capacity for juvenile salmon using quantile random forest models

Abstract Establishing robust methods and metrics to evaluate habitat quality is critical for the recovery of endangered Pacific salmonids ( Oncorhynchus spp.). A variety of modeling approaches are used for status and trend monitoring of anadromous species throughout the Pacific Northwest, USA, but current methods may fail to capture the complex relationship between fish and habitat and are often limited in predictive power beyond specific watersheds. Further, the focus on species distribution and abundance is not easily manipulated to predict carrying capacity and traditional stock‐recruitment analyses are reliant on long‐term data which are not always available. In this study, we developed a quantile random forest model to provide estimates of habitat carrying capacity for Chinook salmon ( O. tshawytscha ) parr during the summer months, at both the site and watershed scale. Quantile random forest models allow for the consideration of noisy data, correlated variables, and non‐linear relationships: common features in fish–habitat datasets. We leveraged Columbia Habitat Monitoring Program data to select habitat co‐variates and predict capacity at those sites. We also identified a set of globally available attributes to extrapolate capacity estimate predictions throughout wadeable streams within the Columbia River basin. Total capacity estimates for watersheds closely matched estimates from alternative fish productivity models. Carrying capacity estimates based on quantile random forest models, like those presented here, provide managers a framework to guide the identification, prioritization, and development of habitat rehabilitation actions to recover salmon populations.

See, Kevin E.↗

DOE OSTI2021

A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients

Abstract Domain decomposition methods have been proved to be an effective strategy to reduce the dimension of parametric partial differential equations (PDEs). However, existing domain decomposition methods for parametric PDEs are usually intrusive, which means domain decomposition based solvers need to be implemented from scratch for each target parametric PDE. To address this issue, we develop a new non‐intrusive domain‐decomposition model reduction method for linear steady‐state PDEs with random‐field coefficients. As a variant of our previous work by Mu and Zhang, the new method only needs access to the final linear system, that is, the global stiffness matrix and the right hand side, of a deterministic PDE solver, in order to build a domain‐decomposition‐based reduced model without intrusive implementation from scratch. The key idea is to remove the interface condition between sub‐domains and rely on the correlation between columns of the linear system to couple the sub‐domains. The non‐intrusive feature enables the applicability of the proposed method to a broader class of uncertainty quantification problems, where many legacy codes/solvers can be fully reused by our method. Two numerical examples including diffusion equations with random diffusivity and convection‐dominated transport with random velocity, are provided to demonstrate the effectiveness and efficiency of our method.

Zhang, Guannan↗

DOE OSTI2024

Approximate CFTs and random tensor models

Abstract A key issue in both the field of quantum chaos and quantum gravity is an effective description of chaotic conformal field theories (CFTs), that is CFTs that have a quantum ergodic limit. We develop a framework incorporating the constraints of conformal symmetry and locality, allowing the definition of ensembles of ‘CFT data’. These ensembles take on the same role as the ensembles of random Hamiltonians in more conventional quantum ergodic phases of many-body quantum systems. To describe individual members of the ensembles, we introduce the notion of approximate CFT, defined as a collection of ‘CFT data’ satisfying the usual CFT constraints approximately, i.e. up to small deviations. We show that they generically exist by providing concrete examples. Ensembles of approximate CFTs are very natural in holography, as every member of the ensemble is indistinguishable from a true CFT for low-energy probes that only have access to information from semi-classical gravity. To specify these ensembles, we impose successively higher moments of the CFT constraints. Lastly, we propose a theory of pure gravity in AdS 3 as a random matrix/tensor model implementing approximate CFT constraints. This tensor model is the maximum ignorance ensemble compatible with conformal symmetry, crossing invariance, and a primary gap to the black-hole threshold. The resulting theory is a random matrix/tensor model governed by the Virasoro 6j-symbol.

Physics↗