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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Neutron (and other Particle) Transport at LANL: An Overview [Presentation]

For decades, Los Alamos National Laboratory has been at the forefront of neutron transport methods research and code development. One such code is PARTISN, the LANL parallel time-dependent discrete ordinate neutron transport code. In this presentation, we describe the various research efforts currently underway by the PARTISN and other code teams. Some examples of current research are a block automated mesh refinement scheme, the application of tensor trains to the discretized neutron transport equation, and GPU code porting. The block automated mesh refinement scheme uses cross section information to refine and coarsen the solution mesh to improve time to solution and reduce memory. The tensor train approach expresses discretized transport operators as tensor products of vectors and matrices to compress the size of linear systems being solved by transport codes. Rather than relying on matrix-free methods such as the transport sweep, we have access to an operator that can be inverted, reshaped, or manipulated algebraically. Finally, we describe how PARTISN is used, what problems we are looking to solve, and what the future holds for neutron transport at LANL. In addition to this, we briefly describe the various research efforts in other particle transport teams using both deterministic and Monte Carlo methods. In the presentation, we list possible opportunities for collaboration between the laboratory and faculty and students.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Preserving Superconvergence of Spectral Elements for Curved Domains via $h$ and $p$-Geometric Refinement

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using h- and p-geometric refinement, which refines the mesh near high-curvature regions and increases the degree of geometric basis functions, respectively. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Chapter 4: Physically informed deep learning networks for simulating microstructure evolution of 3D polycrystals

As discussed in the previous chapter, high energy diffraction microscopy (HEDM) is used to study the micromechanical evolution of a material during in situ loading. HEDM experiments have been used to verify crystal plasticity (CP) simulations [119, 91, 90, 120], for experimental planning, material design, and to further analyze experimental results. However, Fast Fourier transform-based CP (CP-FFT) or finite element-based CP (CP-FE) methods are often too slow to be used in real-time during an experiment. CP-FFT is faster than CP-FE simulations due to the absence of meshing, but can still take hours to simulate the response of a single volume depending on the size and number of strain steps [127]. Reducing computation time would create a larger exploration space in planning and design, and enable faster analysis of experimental results and real-time feedback during an experiment. This research expands upon previous works to develop a workflow for predicting the full-field evolution of a 3D polycrystal. The workflow is simplified from previous works to predict only orientation and elastic strain tensors (from which stress tensors are calculated). The network is physically informed through loss functions and network architecture for a more robust model. The orientation predictions are informed about the cubic crystal symmetry of the material by incorporating disorientation and misorientation information into the network architecture and loss. The Von Mises stress is used to enforce the correct stress-strain trends in the strain tensor predictions. Additional total strain steps from the elastic and elastoplastic region are included to better capture the stress-strain evolution at smaller total strain steps. Material and hardening parameters are additional inputs into the networks to further inform the network and to study the network’s ability to predict different materials other than those used for training.

36 MATERIALS SCIENCE↗
DOE OSTI2024

G2Aero Database of Airfoils - Curated Airfoils

This dataset contains a curated set of 19,164 airfoil shapes from various applications and the data-driven design space of separable shape tensors (PGA space), which can be used as a parameter space for machine-learning applications focused on airfoil shapes. We constructed the airfoil dataset in two main stages. First, we identified 13 baseline airfoils from the NREL 5MW and IEA 15MW reference wind turbines. We reparameterized these shapes using least-squares fits of 8-order CST parametrizations, which involve 18 coefficients. By uniformly perturbing all 18 CST coefficients by +/-20% around each baseline airfoil, we generated 1,000 unique airfoils. Each airfoil was sampled with 1,001 shape landmarks whose x-coordinates followed a cosine distribution along the chord. This process resulted in a total of 13,000 airfoil shapes, each with 1,001 landmarks. In the second phase, we gathered additional airfoils from the extensive BigFoil database, which consolidates data from sources such as the University of Illinois Urbana-Champaign (UIUC) airfoil database, the JavaFoil database, the NACA-TR-824 database, and others. We undertook a thorough pre-processing step to filter out shapes with sparse, noisy, or incomplete data. We also removed airfoils with sharp leading edge and those exceeding our threshold for trailing edge thickness. Additionally, we thinned out the collection of NACA airfoils-- parametric sweeps of NACA airfoils with increasing thickness and camber present in BigFoil database-- by selecting every fourth step in the parameter sweeps. Finally, we regularized the airfoils by reparametrizing them with an 8-order CST parametrization (with 1,001 shape landmarks with x coordinated following cosine distribution along the chord) and removing airfoils with high reconstruction errors. This data pre-processing resulted in a set of 6,164 airfoils. In total, our curated airfoil dataset comprises 19,164 airfoils, each with 1,001 landmarks, and is stored in the curated_airfoils.npz file. Using this curated airfoil dataset, we utilized the separable shape tensors framework to develop a data-driven parameterization of airfoils based on principal geodesic analysis (PGA) of separable shape tensors. This PGA space is provided in PGAspace.npz file.

airfoils↗
DOE OSTI2026

The Kinetic-Energy–Momentum–Mass 5-Flux of a Baryon Fluid in Bargmann Spacetimes

A Bargmann spacetime is a constrained five-dimensional setting that, while introducing no new physical degrees of freedom beyond those of ordinary four-dimensional spacetime, permits Galilei physics to be expressed with a tensor formalism that respects the distinction between mass and energy while affording the conceptual and technical advantages of a spacetime metric. This framework offers a route to a strong-field ‘Galilei general relativity’ approximating the usual Poincaré general relativity introduced by Einstein. In preparation for modeling core-collapse supernovae, where such an approximation would be useful, this work generalizes the kinetic-energy–momentum–mass 5-flux 𝒯 and its associated spacetime tensor law from a simple fluid of constant particle mass to a baryon fluid whose multiple nuclear species can interconvert rest mass and internal energy. The spacetime tensor law on Bargmann–Galilei spacetime 𝐵𝒢 and its decompositions relative to comoving (‘Lagrangian’) and fiducial (‘Eulerian’) observers are derived in detail. The formalism is rendered more suitable for core-collapse supernova modeling by an extension from strict 𝐵𝒢 to a regime that might be denoted as 𝐵𝒢+: microscopically Poincaré yet macroscopically Galilei. This extension accommodates energy generation by nuclear composition changes and allows comoving energy density and pressure to contribute relative to mass density, while preserving the simplifications of Galilei bulk fluid flow and the streamlined geometry governed by the Bargmann–Galilei spacetime metric.

Cardall, Christian [ORNL] (ORCID:000000020086105X)↗
DOE OSTI2023

Aerodynamic Sensitivity of a Novel Data-Driven Airfoil Shape Representation Framework

We explore the aerodynamic implications of a novel data-driven separable shape tensor framework used to represent discrete airfoil shapes. In this study, we construct a data-driven parameter space defined by separable shape tensors and informed by tens of thousands of distinct airfoils. We use this design space to generate new airfoil designs to study parametric sensitivities with respect to various aerodynamic responses. We use a HAM2D RANS solver to approximate the lift, drag, and moment coefficients for the generated airfoils at two different angles-of-attack. We analyze the robustness and sensitivities of using the separable shape tensor design space by examining the coverage of the aerodynamic response space, uncovering low-dimensional polynomial ridge approximations, and computing various sensitivity metrics. The results show that the data-driven design space produce significant variation in target aerodynamic quantities and facilitate highly accurate approximations (R^2 > 0.96) of one- and two-dimensional structures in each aerodynamic response. This further reduces the effective dimension to enable simplified design and optimization tasks.

aerodynamics↗
DOE OSTI2026

First constraints on causal sources of primordial gravitational waves from BICEP/Keck, SPTpol, SPT-3G, Planck and WMAP $B$-mode data

Non-inflationary sources of gravitational waves in the early Universe generically predict causality-limited tensor power spectra at low frequencies. We report the first-ever constraints on such sources based on cosmic microwave background (CMB) $B$-mode polarization measurements. Using data from BICEP/Keck, SPTpol, SPT-3G, Planck, and WMAP, we constrain the amplitude of an early causal tensor (ECT) power spectrum parameterized by $r_{ect}$, the ratio of causal tensor power to total scalar power at $k~=~0.01$ Mpc$^{-1}$, and obtain a 95% CL upper limit of $r_{ect}<$ 0.0077. Since $r_{ect}$ can easily be related to the parameters of a given theory, our bound robustly constrains a broad class of well-motivated gravitational wave sources in the early universe, including first-order cosmological phase transitions, enhanced small-scale density perturbations, and various topological defects. Finally, we translate our limit into a bound on the present-day energy density in gravitational waves at ultra-low frequencies otherwise inaccessible to traditional gravitational wave detection strategies, including pulsar timing arrays, interferometers, and resonant cavities.

Zebrowski, Jessica A. [Fermilab; Chicago U., KICP]↗
DOE OSTI2021

Traversable wormhole solution with a background Kalb–Ramond field

Highlights: • Wormhole solutions of gravity in a Lorentz breaking symmetry scenario are found. • Light deflection by the wormhole in a Lorentz breaking symmetry scenario is calculated. • It is shown the influence of the vacuum expectation value of a Kalb–Ramond field in deflection of light. We obtain a static spherically symmetric wormhole solution due to the vacuum expectation value (vev) of a Kalb–Ramond field. The Kalb–Ramond (vev) is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb–Ramond (vev) and the Ricci tensor, we found an exact traversable wormhole solution sustained by matter sources with a negative isotropic pressure. The matter source satisfies the energy conditions at the throat for particular choices of the LSB parameter. Moreover, we employ the Gauss–Bonnet method to analyze the deflection angle of light in the weak limit approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Characterizing Topological Order with Matrix Product Operators

One of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries of the local tensors that encode the wavefunction. In their most general form, these symmetries are represented by matrix product operators acting on the virtual level, which leads to a set of algebraic rules characterizing states with topological quantum order. This construction generalizes the concepts of $\mathsf G$- and twisted injectivity; the corresponding matrix product operators encode all topological features of the theory and provide a complete picture of the ground state manifold on the torus. We show how the string-net models of Levin and Wen fit within this formalism and in doing so provide a particularly intuitive interpretation of the pentagon equation for F-symbols as the pulling of matrix product operators through the string-net tensor network. Our approach paves the way to finding novel topological phases beyond string nets and elucidates the description of topological phases in terms of entanglement Hamiltonians and edge theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A New Proof That the Number of Linear Elastic Symmetries in Two Dimensions Is Four

In this work, we present an elementary and self-contained proof that there are exactly four symmetry classes of the elasticity tensor in two dimensions: oblique, rectangular, square, and isotropic. In two dimensions, orthogonal transformations are either reflections or rotations. The proof is based on identification of constraints imposed by reflections and rotations on the elasticity tensor, and it simply employs elementary tools from trigonometry, making the proof accessible to a broad audience. For completeness, we identify the sets of transformations (rotations and reflections) for each symmetry class and report the corresponding equations of motions in classical linear elasticity.

42 ENGINEERING↗
DOE OSTI2020

LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory

In this paper, we present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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.↗