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DOE OSTI2024

Bounding irrelevant operators in the 3d Gross-Neveu-Yukawa CFTs

We perform a numerical bootstrap study of scalar operators in the critical 3d Gross-Neveu-Yukawa models, a family of conformal field theories containing N Majorana fermions in the fundamental representation of an O(N) global symmetry. We compute rigorous bounds on the scaling dimensions of the next-to-lowest parity-even and parity-odd singlet scalars at N = 2, 4, and 8. All of these dimensions have lower bounds greater than 3, implying that there are only two relevant singlet scalars and placing constraints on the RG flow structure of these theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2008

Quantum-Inspired Maximizer

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

Zak, Michail↗

DOE OSTI2023

Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model

Here we consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an entanglement phase diagram that resembles that of the Hamiltonian problem in some ways, while being qualitatively different in others. When one type of bond is dominantly measured, we find area-law entangled phases that protect two topological qubits (on a torus) for a time exponential in system size. This generalizes the recently proposed idea of Floquet codes, where logical qubits are dynamically generated by a time-periodic measurement schedule, to a stochastic setting. When all types of bonds are measured with comparable frequency, we find a critical phase with a logarithmic violation of the area law, which sharply distinguishes it from its Hamiltonian counterpart. The critical phase has the same set of topological qubits, as diagnosed by the tripartite mutual information, but protects them only for a time polynomial in system size. Furthermore, we observe an unusual behavior for the dynamical purification of mixed states, characterized at late times by the dynamical exponent z = $\frac{1}{2}$ a superballistic dynamics made possible by measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Novel 2D velocity estimation method for large transient events in plasmas

Dynamics of fast transient events are challenging to be analyzed with high time resolution. Such events can occur in fusion plasmas such as the filaments during edge-localized modes (ELMs). Here, we present a robust method—the spatial displacement estimation—for estimating the displacements of structures with fast dynamics from high spatial and time resolution imaging diagnostics [e.g., gas-puff imaging (GPI)] with sampling time temporal resolution. First, a background suppression method is shown, which suppresses the slowly time-evolving and spatially non-uniform background in the signal. In the second step, a two-dimensional polynomial trend subtraction method is presented to tackle the remaining polynomial order trend in the signal. After performing these pre-processing steps, the spatial displacement of the propagating structure is estimated from the two-dimensional spatial cross-correlation coefficient function calculated between consecutive frames. The method is tested for its robustness and accuracy by simulated Gaussian events and spatially displaced random noise. An example application of the method is presented on propagating ELM filaments measured by the GPI system on the National Spherical Torus Experiment spherical tokamak.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2001

New Data Source for Studying and Modelling the Topside Ionosphere

The existing uncertainties about density profiles in the topside ionosphere, i.e., in the height regime from hmF2 to approx. 2000 km, requires the search for new data sources. Millions of ionograms had been recorded by the ISIS and Alouette satellites in the sixties and seventies, that never were analyzed in terms of electron density profiles. In recent years an effort started to digitize the analog recordings to prepare the ionograms for computerized analysis. This paper shows how the digital ionograms are processed and the electron density profiles (from satellite orbit altitude, 1400 km for ISIS-2, down to the F peak) are calculated. The most difficult part of the task is the automatic scaling of the echo traces in the ISIS ionograms. Unlike the ionograms from modern ionosondes, the ISIS ionograms do not identify the wave polarization of the different echo traces, so physical logic must be applied to identify the ordinary ()) and extraordinary (X) traces, and this is not always successful. Characteristic resonance features seen in the topside ionograms occur at the gyro and plasma frequencies. An elaborate scheme was developed to identify these resonance frequencies in order to determine the local plasma and gyrofrequencies. This information helps in the identification of the O and X traces, and it provides the starting density of the electron density profile. The inversion of the echo traces into electron density profiles uses the same modified Chebyshev polynomial fitting technique that is successfully applied in the ground-based Digisonde network. The automatic topside ionogram scaler with true height algorithm TOPIST is successfully scaling approx. 70% of the ionograms. An 'editing process' is available to manually scale the more difficult ionograms. The home page for the ISIS project is at http://nssdc.gsfc.nasa.gov/space/isis/isis-status.html. It provides access to as of January 2001, 3000,000 digitized ISIS ionogram data and to related software. A search page lets users select data location, time, and a host of other search criteria. The automated processing of the ISIS ionograms will begin later this year and the electron density profiles will be made available from the project home page. The ISIS data restoration efforts are supported through NASA's Applied Systems and Information Research Program.

Huang, Xue-Qin↗

DOE OSTI2025

Image-Driven Hybrid Structural Analysis Based on Continuum Point Cloud Method with Boundary Capturing Technique

Conventional approaches for the structural health monitoring of infrastructures often rely on physical sensors or targets attached to structural members, which require considerable preparation, maintenance, and operational effort, including continuous on-site adjustments. This paper presents an image-driven hybrid structural analysis technique that combines digital image processing (DIP) and regression analysis with a continuum point cloud method (CPCM) built on a particle-based strong formulation. Polynomial regressions capture the boundary shape change due to the structural loading and precisely identify the edge and corner coordinates of the deformed structure. The captured edge profiles are transformed into essential boundary conditions. This allows the construction of a strongly formulated boundary value problem (BVP), classified as the Dirichlet problem. Capturing boundary conditions from the digital image is novel, although a similar approach was applied to the point cloud data. It was shown that the CPCM is more efficient in this hybrid simulation framework than the weak-form-based numerical schemes. Unlike the finite element method (FEM), it can avoid aligning boundary nodes with regression points. A three-point bending test of a rubber beam was simulated to validate the developed technique. The simulation results were benchmarked against numerical results by ANSYS and various relevant numerical schemes. The technique can effectively solve the Dirichlet-type BVP, yielding accurate deformation, stress, and strain values across the entire problem domain when employing a linear strain model and increasing the number of CPCM nodes. In addition, comparative analysis with conventional displacement tracking techniques verifies the developed technique’s robustness. The proposed technique effectively circumvents the inherent limitations of traditional monitoring methods resulting from the reliance on physical gauges or target markers so that a robust and non-contact solution for remote structural health monitoring in real-scale infrastructures can be provided, even in unfavorable experimental environments.

Chemistry↗

DOE OSTI2023

Temporal Subsampling Diminishes Small Spatial Scales in Recurrent Neural Network Emulators of Geophysical Turbulence

The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use data sets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (a) a form of Nonlinear Vector Autoregression (NVAR), and (b) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.

58 GEOSCIENCES↗

DOE OSTI2024

Subsampling of Parametric Models with Bifidelity Boosting

Least squares regression is a ubiquitous tool for building emulators (a.k.a. surrogate models) of problems across science and engineering for purposes such as design space exploration and uncertainty quantification. When the regression data are generated using an experimental design process (e.g., a quadrature grid) involving computationally expensive models, or when the data size is large, sketching techniques have shown promise at reducing the cost of the construction of the regression model while ensuring accuracy comparable to that of the full data. However, random sketching strategies, such as those based on leverage scores, lead to regression errors that are random and may exhibit large variability. To mitigate this issue, we present a novel boosting approach that leverages cheaper, lower-fidelity data of the problem at hand to identify the best sketch among a set of candidate sketches. This in turn specifies the sketch of the intended high-fidelity model and the associated data. We provide theoretical analyses of this bifidelity boosting (BFB) approach and discuss the conditions the low- and high-fidelity data must satisfy for a successful boosting. In doing so, we derive a bound on the residual norm of the BFB sketched solution relating it to its ideal, but computationally expensive, high-fidelity boosted counterpart. Finally, empirical results on both manufactured and PDE data corroborate the theoretical analyses and illustrate the efficacy of the BFB solution in reducing the regression error, as compared to the nonboosted solution.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2001

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa.

Mengshoel, Ole J.↗

DOE OSTI2020

Bi-fidelity Gradient-Based Approach for Nonlinear Well Logging Inverse Problems

Solving a non-linear inverse problem is challenging in computational science and engineering. Sampling based methods require a large number of model valuations; gradientbased methods require fewer model evaluations but only find the local minima. Multifidelity optimization combines the low fidelity model and the high-fidelity model to achieve both high accuracy and high efficiency. In this paper, we present a bi-fidelity approach to solve non-linear inverse problems. In the bi-fidelity inversion method, the low-fidelity model is used to acquire a good initial guess, and the high-fidelity model is used to locate the global minimum. Combined with a multi-start optimization scheme, the proposed approach significantly increases the possibility of finding the global minimum for nonlinear inverse problems with many local minima. The method is tested with two toy problems and then applied to an electromagnetic well logging inverse problem, which is difficult to solve using traditional gradient-based methods. The bi-fidelity method provides promising inversion results and can be easily applied to traditional gradient-based methods.

42 ENGINEERING↗

DOE OSTI2024

Zero modes of massive fermions delocalize from axion strings

Massless chiral excitations can arise from the interactions between a fermion and an axion string, propagating along the string and allowing it to superconduct. The properties of these excitations, or zero modes, dictate how the string interacts with light and can thus have important phenomenological consequences. In this paper, we add a nowhere-vanishing Dirac mass for the fermion in the usual model of axion electrodynamics. We find that the zero modes exhibit an interesting phase structure in which they delocalize from the string’s core as the mass increases, up until a critical value past which they disappear. We study this structure from an analytic perspective, with explicit numerical solutions, and via anomaly inflow arguments. Finally, we derive the two-dimensional effective theory of the zero mode and its interactions with the four-dimensional gauge field and show how this effective theory breaks down as the zero modes delocalize.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2018

Quantification of Error Associated with Using Misaligned Meshes in Continuum Damage Mechanics Material Models for Matrix Crack Growth Predictions in Composites

The ability of a material model to capture in-plane matrix mode I and mode II crack growth is an essential component for modeling ply level damage evolution in composite structures. Previous studies using a continuum damage mechanics (CDM) approach have shown success in satisfying benchmark solutions for mode I and II crack growth. However, success was shown using a fiber-aligned meshing strategy, which encourages matrix cracks to propagate in a single band of elements, along the fiber direction. Generating a fiber-aligned mesh becomes a highly involved process for laminates including off-axis (non 0° or 90°) plies. The objective of this study is to quantify the effect of non-fiber aligned mesh discretization on predictions of in-plane matrix crack propagation. The approach taken incrementally varies the mesh orientation angle relative to the fiber orientation; more specifically, misaligned meshes are used to quantify the effect of element angle orientation relative to the initial crack orientation on the energy released during matrix crack propagation simulations using a CDM method. CDM solutions obtained with the misaligned meshes are evaluated against known benchmarks for mode I and II matrix crack growth. The CDM solutions reveal a near-polynomial trend of increased predicted failure stress with increased mesh misalignment angle; hence implying a potential relationship between element orientation angle and apparent fracture toughness.

Justusson, Brian↗

DOE OSTI2026

DESI DR2 Galaxy luminosity functions

We present galaxy luminosity functions (LFs) for the Dark Energy Spectroscopic Instrument (DESI) DR2 Bright Galaxy Survey (BGS) in the g, r, z, and $w1$ bands over $0.002\lt z\lt 0.6$. Our analysis uses updated k-corrections and evolutionary corrections, including new polynomial kcorrection fits derived from BGS Year 1 data that supersede earlier GAMA-based prescriptions. Exploiting the statistical power of DESI, we measure LFs to very faint magnitudes, reaching $^{0.1}M_r-5\log h\sim -10$. Independent measurements from the North and South survey regions show excellent agreement around the LF knee, but the very small statistical uncertainties reveal that simple analytic forms fail to capture the full LF shape. The bright end departs from a pure exponential decline, while the faint end exhibits complex, non-powerlaw behaviour, including a pronounced upturn at $^{0.1}M_r-5\log h\gtrsim -15$, which is stronger for red galaxies than for blue. We show that our LFs are largely complete for galaxies with surface brightness $\mu _{50}\lt 25$, and that an apparent steepening fainter than $-13$ is driven primarily by local overdensity and fragmentation of large galaxies. A systematic North–South offset at the brightest magnitudes is traced to red galaxies and may reflect shallower North photometry underestimating extended earlytype profiles, although this remains inconclusive. We therefore also provide LFs based on model Petrosian magnitudes. Redshift splitting reveals small but significant residuals, indicating limitations of a simple global evolutionary model. Using the redshift limits of J. Loveday et al. (2012), we find excellent agreement with GAMA, with substantially reduced statistical errors. These measurements provide a precise reference for studies of environmental and population-dependent LFs and for testing galaxy formation models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Kernel Manifolds: Nonlinear‐Augmentation Dimensionality Reduction Using Reproducing Kernel Hilbert Spaces

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections, augment linear dimensionality reduction with a nonlinear correction term in the reconstruction map to overcome approximation accuracy limitations of purely linear approaches. While feature map-based approaches typically learn a least squares optimal polynomial correction term, we generalize this approach by learning an optimal nonlinear correction from a user-defined reproducing kernel Hilbert space. Our approach allows one to impose arbitrary nonlinear structure on the correction term, including polynomial structure, and includes feature map and radial basis function-based corrections as special cases. Furthermore, our method has relatively low training cost and has monotonically decreasing error as the latent space dimension increases. In conclusion, we compare our approach to proper orthogonal decomposition and several recent QM approaches on data from several example problems.

kernel methods↗

NASA NTRS2005

Influence of a fat layer on the near infrared spectra of human muscle: quantitative analysis based on two-layered Monte Carlo simulations and phantom experiments

The influence of fat thickness on the diffuse reflectance spectra of muscle in the near infrared (NIR) region is studied by Monte Carlo simulations of a two-layer structure and with phantom experiments. A polynomial relationship was established between the fat thickness and the detected diffuse reflectance. The influence of a range of optical coefficients (absorption and reduced scattering) for fat and muscle over the known range of human physiological values was also investigated. Subject-to-subject variation in the fat optical coefficients and thickness can be ignored if the fat thickness is less than 5 mm. A method was proposed to correct the fat thickness influence. c2005 Optical Society of America.

NASA Discipline Life Sciences Technologies↗

NASA NTRS2000

Phase Screen Determination for the GeoSAR Interferometric Mapping Instrument

GeoSAR is a dual frequency airborne radar interferometric mapping instrument designed to obtain high resolution and high accuracy digital elevation models. The X-band inteferometric antennas are mounted beneath the fuselage with a separation distance of 2.6 m. Midway between the antennas along the aircraft centerline is a large fairing housing the Laser Baseline metrology System (LBMS) and Inertial Navigtion Units (INUs). The P-band antennas are mounted in wingtip pods approximately 10 m from the aircraft centerline. Multipath signals reflected from the LBMS fairing cause phase distortions corrupting the topograhic height measurements for both the X-band and P-band systems. In addition multipath off the wing affects the P-band phase measurements. In this paper we discuss a technique used to mitigate the amount of X-Band multipath and methods calibrating and correcting the phase for both X-Band and P-Band using a high accuracy DEM. Height differences between the interferometrically derived elevations and a photogrammetrically derived DEM are converted into phase differences. Multipath phase errors are sinusoidal with spatial frequency and amplitude related to the magnitude of reflection of the multipath reflection point and its distance from the interferometric antennas. These phase residuals are fitted using a Chebyshev polynomial sequence and used as a phase screen in the processor to correct the phase prior to height reconstruction. Based on the correction signal it is possible to estimate the location and magnitude of the multipath signal. This information can then be used to extend the domain of the phase screen over mapping angles not covered during the calibration passes. Keywords: SAR,interferometry,phase screen

Hensley, Scott↗

DOE OSTI2022

An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2018

A Blueprint for Demonstrating Quantum Supremacy with Superconducting Qubits

Long coherence times and high fidelity control recently achieved in scalable superconducting circuits paved the way for the growing number of experimental studies of many-qubit quantum coherent phenomena in these devices. Albeit full implementation of quantum error correction and fault tolerant quantum computation remains a challenge the near term pre-error correction devices could allow new fundamental experiments despite inevitable accumulation of errors. One such open question foundational for quantum computing is achieving the so called quantum supremacy, an experimental demonstration of a computational task that takes polynomial time on the quantum computer whereas the best classical algorithm would require exponential time and/or resources. It is possible to formulate such a task for a quantum computer consisting of less than a 100 qubits. The computational task we consider is to provide approximate samples from a non-trivial quantum distribution. This is a generalization for the case of superconducting circuits of ideas behind boson sampling protocol for quantum optics introduced by Arkhipov and Aaronson. In this presentation we discuss a proof-of-principle demonstration of such a sampling task on a 9-qubit chain of superconducting gmon qubits developed by Google. We discuss theoretical analysis of the driven evolution of the device resulting in output approximating samples from a uniform distribution in the Hilbert space, a quantum chaotic state. We analyze quantum chaotic characteristics of the output of the circuit and the time required to generate a sufficiently complex quantum distribution. We demonstrate that the classical simulation of the sampling output requires exponential resources by connecting the task of calculating the output amplitudes to the sign problem of the Quantum Monte Carlo method. We also discuss the detailed theoretical modeling required to achieve high fidelity control and calibration of the multi-qubit unitary evolution in the device. We use a novel cross-entropy statistical metric as a figure of merit to verify the output and calibrate the device controls. Finally, we demonstrate the statistics of the wave function amplitudes generated on the 9-gmon chain and verify the quantum chaotic nature of the generated quantum distribution. This verifies the implementation of the quantum supremacy protocol.

Kechedzhi, Kostyantyn↗