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At least 433 records · Page 24

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DOE OSTI2025

A review of low-rank methods for time-dependent kinetic simulations

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Efficient CP Rounding Using Alternating Least Squares with QR Decomposition

The CANDECOMP/PARAFAC (CP) decomposition is widely used for analyzing multidimensional data, and the alternating least squares (CP-ALS) algorithm is a common method for its computation. CP rounding is the problem of computing a lower-rank CP decomposition of an input already in a higher-rank CP format. While the normal equations (NE) approach in CP-ALS is efficient for the CP rounding problem and frequently used, it becomes unstable in the presence of ill-conditioned subproblems. This paper presents a new QR-based CP-ALS method for CP rounding that preserves both numerical stability and computational efficiency. Here, our experiments show that the proposed method offers significant speedup over a previous QR-based approach and the Tensor Toolbox's NE-based implementation, particularly for higher-order tensors. Furthermore, our approach demonstrates a marked reduction in error for ill-conditioned problems, with error reductions several orders of magnitude smaller compared to the NE-based method, while achieving faster convergence and more accurate solutions. By using a more numerically stable approach, we can solve more problems in reduced working precision, which enables further reduction in time to solution.

CANDECOMP/PARAFAC↗

DOE OSTI2025

Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems

Strongly-correlated quantum many-body systems are difficult to study and simulate classically. We recently proposed a variational quantum eigensolver (VQE) based on the multiscale entanglement renormalization ansatz (MERA) with tensors constrained to certain Trotter circuits. Here, we determine the scaling of computation costs for various critical spin chains which substantiates a polynomial quantum advantage in comparison to classical MERA simulations based on exact energy gradients or variational Monte Carlo. Algorithmic phase diagrams suggest an even greater separation for higher-dimensional systems. Hence, the Trotterized MERA VQE is a promising route for the efficient investigation of strongly-correlated quantum many-body systems on quantum computers. Furthermore, we show how the convergence can be substantially improved by building up the MERA layer by layer in the initialization stage and by scanning through the phase diagram during optimization. For the Trotter circuits being composed of single-qubit and two-qubit rotations, it is experimentally advantageous to have small rotation angles. We find that the average angle amplitude can be reduced considerably with negligible effect on the energy accuracy. Benchmark simulations suggest that the structure of the Trotter circuits for the TMERA tensors is not decisive; in particular, brick-wall circuits and parallel random-pair circuits yield very similar energy accuracies.

Miao, Qiang [Duke Quantum Center, Duke University,↗

DOE OSTI2026

Crystal Orientation Independent Strong TERS Response in Anisotropic ReS2 on Gold

Rhenium disulfide (ReS2) crystallizes in a distorted 1T' lattice with triclinic symmetry arising from Re–Re dimerization, which produces in-plane anisotropic properties and a dense set of Raman-active modes with mixed atomic displacements. Unlike far-field Raman spectroscopy, which shows strong polarization and orientation dependence, tip-enhanced Raman spectroscopy (TERS) probes out-of-plane Raman tensor components. Here we use 785 nm (1.58 eV) gap-mode TERS to investigate monolayer to four-layer thick ReS2 crystals.. TERS maps and averaged spectra reveal that all modes remain invariant under 90° rotation of the crystal, and the only thickness-dependent feature is the emergence of the multilayer breathing mode. These results demonstrate that TERS yields a crystal-orientation-independent Raman response in ReS2 and provides direct access to Raman tensor components that are not easily accessible in conventional far-field measurements.

Valencia Acuna, Pavel A.↗

DOE OSTI2024

Angle-Resolved Polarized Raman Study of Layered Cr 2 Se 3

The polarization-resolved Raman spectra of two-dimensional Cr 2 Se 3 synthesized via chemical vapor deposition (CVD) and chemical vapor transport (CVT) techniques were investigated in detail. The samples were characterized using X-ray diffraction (XRD), transmission electron microscopy (TEM), and energy-dispersive X-ray spectroscopy (EDS). A distinct polarization dependence was observed in the Raman intensity of all the Cr-Cr, Cr-Se, and Se-Se modes in both samples. The observed angle-dependent Raman intensities of each peak could be related to the crystal structure-specific Raman tensor. XRD results of the bulk Cr 2 Se 3 sample synthesized via CVT confirm its trigonal crystal structure, and the Raman peaks can be fitted using the Raman tensors for the A g and E g modes for both the parallel and crossed polarizations. However, for the Cr 2 Se 3 samples directly grown on Si/SiO 2 substrates by CVD, it was necessary to assume the triclinic crystal structure in order to explain the polarized Raman dependence of all the peaks in both parallel and crossed polarization directions. Furthermore, this is the first experimental result suggesting the existence of triclinic Cr 2 Se 3 crystal structure, which has been theoretically predicted in the Materials Project database.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Second‐ and Third‐Order Elastic Constants of Inert and Energetic Molecular Crystals From Density Functional Theory

Complete tensors of the second- and third-order elastic constants of the organic molecular crystals acetaminophen, pentaerythritol tetranitrate (PETN), cyclotrimethylene trinitramine (RDX), cyclotetramethylene tetranitramine (HMX), 1,1-diamino-2,2-dinitroethylene (FOX-7), hexanitrohexaazaisowurtzitane (CL-20), and erythritol tetranitrate (ETN) have been calculated using dispersion-corrected density functional theory. The sets of second- and third-order elastic constants are expected to provide a more accurate and reliable description of the behavior of these materials under nonhydrostatic loads than pressure- and volume-dependent second-order elastic constants. The tensors of second-order constants have been compared with experimental data and/or other calculations when possible, and with the exception of results for CL-20 from Brillouin scattering experiments, we find good agreement. The calculated third-order elastic constants of PETN are in very good agreement with the subset of third-order constants derived from experimental wave speed measurements. The elastic anisotropies of the crystals have been estimated using the universal elastic anisotropy index, which shows that the crystals fall into three groups with low anisotropy (PETN, RDX, and CL-20), moderate anisotropy (acetaminophen, HMX, and ETN), and high elastic anisotropy (FOX-7).

36 MATERIALS SCIENCE↗

DOE OSTI2025

cymyc: $\underline{C}$alabi-$\underline{Y}$au $\underline{M}$etrics, $\underline{Y}$ukawas, and $\underline{C}$urvature

We introduce cymyc, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. cymyc includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.

differential and algebraic geometry↗

DOE OSTI2024

Cosmological implications of Kalb-Ramond-like particles

The Kalb-Ramond field is an antisymmetric, rank-two tensor field which most notably appears in the context of string theory, but has largely been unexplored in the context of cosmology. In this work, motivated by the Kalb-Ramond field in string theory, and antisymmetric tensor fields that emerge in effective field theories ranging from particle physics to condensed matter, we study the primordial production of interacting massive Kalb-Ramond-like-particles (KRLPs). KRLPs contain features of both dark photon and axion models, which can be appreciated via their duality properties. While the massless non-interacting KRLP is dual to a pseudoscalar, and the massive non-interacting KRLP is dual to a pseudovector, the interacting massive KRLP can be distinguished from its scalar and vector counterparts. We study early-universe production of KRLPs via the freeze-in mechanism, considering a ‘dark photon-like’ interaction, an ‘axion-like’ interaction, and a ‘Higgs portal’ interaction, as well as production via cosmological gravitational particle production. We find that as a dark matter candidate, KRLPs can be produced by all of the above mechanisms and account for the relic density of dark matter today for a wide range of masses. Finally, we comment on the potential to obtain both warm and cold dark matter subcomponents, and speculate on observational and experimental prospects.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Higher-derivative corrections in M-theory from precision numerical bootstrap

We study higher-derivative corrections to the graviton scattering amplitude in M-theory, via the stress tensor correlator of 3d$\mathcal{N}$= 8 U(N) k × U(N) –k ABJM theory (dual to graviton scattering in M-theory on AdS 4 × S 7 /ℤ k ). We use the conformal bootstrap combined with an integral constraint derived from supersymmetric localization in order to constrain semishort OPE coefficients appearing in the stress tensor correlator. We obtain islands that are significantly more precise than those in previous studies that did not use the integral constraint. Using these islands, we can estimate the powers and coefficients in a large central charge expansion. This allows us to accurately read off the N 3 LO contribution, from the protected D 6 R 4 correction, and also estimate the N 4 LO contribution, from the unprotected D 8 R 4 correction.

AdS-CFT correspondence↗

DOE OSTI2025

Hollow-grams: generalized entanglement wedges from the gravitational path integral

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the “hollowed” RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy Sn depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n → 1 limit.

2D Gravity↗

DOE OSTI2025

Non-invertible defects from the Conway SCFT to K3 sigma models. Part I. General results

We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module V f♮ . We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of $\mathbb{Z}$-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four-plane-preserving TDLs in V f♮ and supersymmetry-preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models.

Conformal Field Models in String Theory↗

DOE OSTI2025

Open-closed 3d gravity as a random ensemble

We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. As an application, we construct a purely open variant of the tensor model to study a purely open bootstrap problem in the context of CFT triangulation. We also briefly discuss the extension to non-orientable CFTs.

AdS-CFT correspondence↗

DOE OSTI2026

Commuting embeddings for parallel strategies in non-local games

Non-local games provide a versatile framework for probing quantum correlations and for benchmarking the power of entanglement. In finite dimensions, the standard method for playing several games in parallel requires a tensor product of the local Hilbert spaces, which scales additively in the number of qubits. In this work, we show that this additive cost can be reduced by exploiting algebraic embeddings. We introduce two forms of compressions. First, when a referee selects one game from a finite collection of games at random, the game quantum strategy can be implemented using a maximally entangled state of dimension equal to the largest individual game, thereby eliminating the need for repeated state preparations. Second, we establish conditions under which several games can be played simultaneously in parallel on fewer qubits than the tensor product baseline. These conditions are expressed in terms of commuting embeddings of the game algebras. Moreover, we provide a constructive framework for building such embeddings. Using tools from Lie theory, we show that aligning the various game algebras into a common Cartan decomposition enables such a qubit reduction. Beyond the theoretical contribution, our framework casts NLGs as algebraic primitives for distributed and resource-constrained quantum computations and suggested NLGs as a comparable device-independent dimension witness.

Commuting embeddings↗

DOE OSTI2026

Lagrange-Remap strategy for multi-material fluid-solid simulations using compressive limiters

In the present work, the Lagrange-Remap strategy proposed in [1] is extended to multi-material fluid-solid simulations. Both hypo-elastic and hyper-elastic material models are considered to describe the mechanical behavior of the solids. In practice, the deviatoric stress tensor (for hypo-elastic materials) and the left Cauchy-Green tensor (for isotropic hyper-elastic materials) are remapped, while the use of compressive limiters effectively reduces numerical diffusion during the remapping step. The simplicity of this diffuse interface approach is emphasized in the context of multi-material fluid-solid simulations. A series of Lagrange-Remap test cases, involving both solids and fluids, are conducted and compared with reference Lagrangian simulations, demonstrating the robustness and accuracy of the overall numerical strategy.

Compressive limiters↗

DOE OSTI2024

The use of digital thread for reconstruction of local fiber orientation in a compression molded pin bracket via deep learning

A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. Further, the MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10%. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11%. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.

42 ENGINEERING↗

DOE OSTI2024

A collision operator for describing dissipation in noncanonical phase space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in a thermodynamic equilibrium described by a Maxwell–Boltzmann distribution. However, the time scale required to reach Maxwell–Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell–Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

Boltzmann equation↗

DOE OSTI2026

Solid state 59 Co NMR study of a Np(VII) compound

Np(VII) compounds with [Co(NH 3 ) 6 ] 3+ cations were synthesized and structurally examined using powder X-ray diffraction. Multiple phases were observed, consisting of octahedral [Co(NH 3 ) 6 ] 3+ cations, discrete tetragonal bipyramidal [NpO 4 (OH) 2 ] 3− anions, and waters of hydration. Electric field gradient tensors at Co sites were measured by solid state 59 Co nuclear magnetic resonance (NMR) spectroscopy and compared with theoretical calculations. The relative contributions of the chemical shift and electric field tensors to the NMR lineshape were determined by recording spectra at field strengths of 7.04 and 11.74 Tesla. Further, the evolution of structure and morphology as a function of sample age and the effects on NMR spectral parameters has also been investigated. These results demonstrate the use of NMR at multiple fields to expand understanding of the stability and electronic structure of high valent neptunium compounds.

heptavalent neptunium↗

DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗