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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Validation of the DESI 2024 Lyα forest BAO analysis using synthetic datasets

The first year of data from the Dark Energy Spectroscopic Instrument (DESI) contains the largest set of Lyman-α (Lyα) forest spectra ever observed. This data, collected in the DESI Data Release 1 (DR1) sample, has been used to measure the Baryon Acoustic Oscillation (BAO) feature at redshift z = 2.33. In this work, we use a set of 150 synthetic realizations of DESI DR1 to validate the DESI 2024 Lyα forest BAO measurement presented in [1]. The synthetic data sets are based on Gaussian random fields using the log-normal approximation. We produce realistic synthetic DESI spectra that include all major contaminants affecting the Lyα forest. The synthetic data sets span a redshift range 1.8 < z < 3.8, and are analyzed using the same framework and pipeline used for the DESI 2024 Lyα forest BAO measurement. To measure BAO, we use both the Lyα auto-correlation and its cross-correlation with quasar positions. We use the mean of correlation functions from the set of DESI DR1 realizations to show that our model is able to recover unbiased measurements of the BAO position. We also fit each mock individually and study the population of BAO fits in order to validate BAO uncertainties and test our method for estimating the covariance matrix of the Lyα forest correlation functions. Finally, we discuss the implications of our results and identify the needs for the next generation of Lyα forest synthetic data sets, with the top priority being to simulate the effect of BAO broadening due to non-linear evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis

ABSTRACT Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On non-linear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

The 3D Lyman- α forest power spectrum from eBOSS DR16

We measure the three-dimensional power spectrum (P3D) of the transmitted flux in the Lyman-α (Ly α) forest using the complete extended Baryon Oscillation Spectroscopic Survey data release 16 (eBOSS DR16). This sample consists of ~205 000 quasar spectra in the redshift range 2 ≤ z ≤ 4 at an effective redshift z = 2.334. We propose a pair-count spectral estimator in configuration space, weighting each pair by exp( i k ∙ r), for wave vector k and pixel pair separation r, effectively measuring the anisotropic power spectrum without the need for fast Fourier transforms. This accounts for the window matrix in a tractable way, avoiding artefacts found in Fourier-transform based power spectrum estimators due to the sparse sampling transverse to the line of sight of Ly α skewers. We extensively test our pipeline on two sets of mocks: (i) idealized Gaussian random fields with a sparse sampling of Ly α skewers, and (ii) log-normal LyaCoLoRe mocks including realistic noise levels, the eBOSS survey geometry and contaminants. On eBOSS DR16 data, the Kaiser formula with a non-linear correction term obtained from hydrodynamic simulations yields a good fit to the power spectrum data in the range $(0.02 ≤ k ≤ 0.35)$ h Mpc -1 at the 1–2σ level with a covariance matrix derived from LyaCoLoRe mocks. We demonstrate a promising new approach for full-shape cosmological analyses of Ly α forest data from cosmological surveys such as eBOSS, the currently observing Dark Energy Spectroscopic Instrument and future surveys such as the Prime Focus Spectrograph, WEAVE-QSO, and 4MOST.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Maximum a posteriori Ly α estimator (MAPLE): band power and covariance estimation of the 3D Ly α forest power spectrum

We present a novel maximum a posteriori estimator to jointly estimate band powers and the covariance of the three-dimensional power spectrum (P3D) of Ly $\alpha$ forest flux fluctuations, called MAPLE. Our Wiener-filter based algorithm reconstructs a window-deconvolved P3D in the presence of complex survey geometries typical for Ly $\alpha$ surveys that are sparsely sampled transverse to and densely sampled along the line of sight. We demonstrate our method on idealized Gaussian random fields with two selection functions: (i) a sparse sampling of 30 background sources per square degree designed to emulate the current Dark Energy Spectroscopic Instrument; (ii) a dense sampling of 900 background sources per square degree emulating the upcoming Prime Focus Spectrograph Galaxy Evolution Survey. Our proof-of-principle shows promise, especially since the algorithm can be extended to marginalize jointly over nuisance parameters and contaminants, i.e. offsets introduced by continuum fitting. Our code is implemented in JAX and is publicly available on GitHub.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions

Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by f NL ⁠, the amplitude of the quadratic correction to the potential of a Gaussian random field, is traditionally measured from LSS two-point and three-point clustering via the power spectrum and bi-spectrum. We propose a framework to measure f NL using the configuration space two-point correlation function (2pcf) monopole and three-point correlation function (3pcf) monopole of survey tracers. Our model estimates the effect of the scale-dependent bias induced by the presence of PNG on the 2pcf and 3pcf from the clustering of simulated dark matter haloes. We describe how this effect may be scaled to an arbitrary tracer of the cosmological matter density. The 2pcf and 3pcf of this tracer are measured to constrain the value of f NL ⁠. In LSS surveys, the effect of imaging systematics on two-point statistics is often degenerate with the PNG signal. Our proposed model employs three-point statistics primarily to break this degeneracy. Using simulations of luminous red galaxies observed by the Dark Energy Spectroscopic Instrument (DESI), we demonstrate the accuracy and constraining power of our method. Our forecast indicates the ability to constrain f NL to a precision of σf NL ≈ 22 with one year of DESI survey data, as well as the ability to constrain the imaging systematic weights in situ.

early Universe↗
DOE OSTI2021

Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered interacting quantum spin chain

Here, we consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL) and add a Markovian dephasing bath coupled to the Anderson orbitals of the model's noninteracting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady-state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath and provides a classical analog for the MBL transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Charge-4e Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene

We show that unconventional nematic superconductors with multicomponent order parameter in lattices with three- and sixfold rotational symmetries support a charge-4e vestigial superconducting phase above T c . The charge-4e state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is nonsuperconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-4e state over the nematic phase, as it acts as a random mass to the former but as a random field to the latter. Furthermore, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-4e superconducting phase.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Phenomenology of Spectral Functions in Disordered Spin Chains at Infinite Temperature

Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Cooperative spin coupling in PrFeO3

A transition from crystal-field to spin wave excitations has been experimentally observed in PrFeO3 using inelastic neutron scattering. Theoretical modeling with density functional theory and the mean field random phase approximation successfully reproduces the experimental observations and allows extraction of the values for the various exchange interactions. The study reveals that the strong coupling between the two magnetic sublattices of Pr and Fe is the fundamental mechanism underlying the low-temperature Pr magnetism. This coupling, analogous to the Dicke cooperative interaction between atoms and photons, polarizes the Pr moments, enhances the Pr-Pr interactions, and contributes to the formation of a quasidoublet, leading to the transition from single-particle to collective excitations within the Pr sublattice. Furthermore, this coupling induces spin reorientation on the Fe sublattice. The manipulation of magnetic moments via spin waves is achievable through the coupling between different magnetic sublattices in a bulk material containing multiple magnetic ions.

Garlea, Vasile [ORNL] (ORCID:0000000253227271)↗
DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗
DOE OSTI2022

A Statistical Interpolation Code for Ocean Analysis and Forecasting

Abstract We present a data assimilation package for use with ocean circulation models in analysis, forecasting, and system evaluation applications. The basic functionality of the package is centered on a multivariate linear statistical estimation for a given predicted/background ocean state, observations, and error statistics. Novel features of the package include support for multiple covariance models, and the solution of the least squares normal equations either using the covariance matrix or its inverse—the information matrix. The main focus of this paper, however, is on the solution of the analysis equations using the information matrix, which offers several advantages for solving large problems efficiently. Details of the parameterization of the inverse covariance using Markov random fields are provided and its relationship to finite-difference discretizations of diffusion equations are pointed out. The package can assimilate a variety of observation types from both remote sensing and in situ platforms. The performance of the data assimilation methodology implemented in the package is demonstrated with a yearlong global ocean hindcast with a 1/4° ocean model. The code is implemented in modern Fortran, supports distributed memory, shared memory, multicore architectures, and uses climate and forecasts compliant Network Common Data Form for input/output. The package is freely available with an open source license from www.tendral.com/tsis/ .

Srinivasan, Ashwanth↗
DOE OSTI2026

Multitask graph neural networks for elastoplastic response prediction in dual-phase polycrystals

Microstructure-sensitive prediction of elastoplastic response remains a recurring bottleneck in multiscale damage and fatigue modeling, where large ensembles of statistically distinct polycrystals are required to quantify variability and extreme-value behavior. In this work, we develop a multitask graph neural network (GNN) surrogate that maps dual-phase ferrite–martensite polycrystal microstructures to Statistical Volume Element (SVE)-level elastoplastic Quantities of Interest (QoIs). Each SVE is represented as a grain-adjacency graph, with node features encoding phase, geometry, and crystallographic orientation, and edge features encoding relative misorientation. A message-passing graph convolution generates node embeddings, which are pooled into a graph representation and passed to a multitask regression head that jointly predicts 10 scalar QoIs and vector-valued stress–strain responses in orthogonal loading directions across multiple martensite volume fractions and SVE sizes. Results show high accuracy for scalar QoIs and strong agreement for full stress–strain trajectories, with population envelopes reproducing both median behavior and finite-SVE variability across compositions and partition scales. A unified model trained on pooled volume-fraction data preserves most within-regime accuracy relative to regime-specific models while also capturing the broader cross-regime variation reflected in the pooled test set. Distributional comparisons further demonstrate that the surrogate preserves heterogeneity under SVE partitioning, enabling statistically consistent block-wise random-field construction for mesoscale analyses. Overall, the proposed grain-graph surrogate provides a practical pathway to accelerate ensemble-based studies of SVE-level constitutive variability in dual-phase polycrystals.

Crystal plasticity↗
DOE OSTI2025

Covariance operator estimation: Sparsity, lengthscale, and ensemble Kalman filters

This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of the covariance and the expected supremum of the field. We prove that thresholded estimators enjoy an exponential improvement in sample complexity compared with the standard sample covariance estimator if the field has a small correlation lengthscale. As an application of the theory, we study thresholded estimation of covariance operators within ensemble Kalman filters.

Covariance operator estimation↗
DOE OSTI2022

A Universal Power-law Prescription for Variability from Synthetic Images of Black Hole Accretion Flows

We present a framework for characterizing the spatiotemporal power spectrum of the variability expected from the horizon-scale emission structure around supermassive black holes, and we apply this framework to a library of general relativistic magnetohydrodynamic (GRMHD) simulations and associated general relativistic ray-traced images relevant for Event Horizon Telescope (EHT) observations of Sgr A*. We find that the variability power spectrum is generically a red-noise process in both the temporal and spatial dimensions, with the peak in power occurring on the longest timescales and largest spatial scales. When both the time-averaged source structure and the spatially integrated light-curve variability are removed, the residual power spectrum exhibits a universal broken power-law behavior. On small spatial frequencies, the residual power spectrum rises as the square of the spatial frequency and is proportional to the variance in the centroid of emission. Beyond some peak in variability power, the residual power spectrum falls as that of the time-averaged source structure, which is similar across simulations; this behavior can be naturally explained if the variability arises from a multiplicative random field that has a steeper high-frequency power-law index than that of the time-averaged source structure. We briefly explore the ability of power spectral variability studies to constrain physical parameters relevant for the GRMHD simulations, which can be scaled to provide predictions for black holes in a range of systems in the optically thin regime. We present specific expectations for the behavior of the M87* and Sgr A* accretion flows as observed by the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Compressive Neural Representations of Volumetric Scalar Fields

Here, we present an approach for compressing volumetric scalar fields using implicit neural representations. Our approach represents a scalar field as a learned function, wherein a neural network maps a point in the domain to an output scalar value. By setting the number of weights of the neural network to be smaller than the input size, we achieve compressed representations of scalar fields, thus framing compression as a type of function approximation. Combined with carefully quantizing network weights, we show that this approach yields highly compact representations that outperform state-of-the-art volume compression approaches. The conceptual simplicity of our approach enables a number of benefits, such as support for time-varying scalar fields, optimizing to preserve spatial gradients, and random-access field evaluation. We study the impact of network design choices on compression performance, highlighting how simple network architectures are effective for a broad range of volumes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Measuring representative volume elements from high-resolution grain-scale strain fields

Most crystalline materials present a highly heterogeneous response at the microscale, which can be affected by both internal factors (such as microstructural parameters) and external factors (such as loading). Relating microscale inhomogeneities to the macroscale response of a material requires the use of homogenisation techniques, usually based on the concept of a representative volume element (RVE)—the smallest volume of material that represents the global average response. Here, in this work, we present a new and robust experimental method of measuring the size of a strain-based RVE from high-resolution grain-scale strain fields obtained using digital image correlation (DIC). The proposed method is based on the statistical (stereological) nature of the RVE, which has been widely adopted in numerical studies, and involves dividing a strain field into randomly selected regions of varying sizes and statistically analysing the distributions of average strains within them. To validate the new method, we generate a large number of synthetic strain fields from a fractional Gaussian noise algorithm. The proposed stereological method is shown to be capable of producing reliable RVE measurements from a very large range of possible microscale strain fields while at the same time being robust in that it can produce RVE measurement results even in cases where other existing methods may be unable to do so. The proposed method has a low field-of-view requirement, only needing a field-of-view about 1.2 times as large as the RVE to produce reliable measurements. In addition, the stereological method offers significant flexibility since its statistical nature allows for control over how strict the RVE measurement should be in each case.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Bringing randomized algorithms to mainstream numerical linear algebra

Numerical linear algebra (NLA) underpins huge swaths of computational science and engineering. For scientists and engineers to make the most of the DOE’s computing resources, it is essential that they have access to high-performance implementations of algorithms with best-in-class scalability and reliability. Despite this, prevailing NLA libraries have little to no support for breakthrough algorithms from the field of randomized numerical linear algebra (RandNLA) that have been developed over the past twenty years. The goal of this LDRD was to break a log-jam that had prevented broad adoption of RandNLA. Our work had two thrusts. The first was to develop RandBLAS: a trustworthy and high-performance C++ library for randomized dimension reduction (an operation widely known as sketching). The second was the development of a novel randomized algorithm for computing a challenging type of matrix decomposition known as Householder QR with column pivoting (Householder QRCP). In this one-year late-start LDRD we successfully delivered RandBLAS 1.0 and new CPU and GPU codes for Householder QRCP. RandBLAS has extensive documentation at https://randblas.readthedocs.io/en/stable/. Papers on RandBLAS and and our high-performance QRCP codes are forthcoming.

97 MATHEMATICS AND COMPUTING↗