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DOE OSTI2024

Krylov spaces for truncated spectrum methodologies

We propose herein an extension of truncated spectrum methodologies, a nonperturbative numerical approach able to elucidate the low energy properties of quantum field theories. TSMs, in their various flavors, involve a division of a computational Hilbert space, H , into two parts, one part, H 1 that is “kept” for the numerical computations, and one part, H 2 , that is discarded or “truncated.” Even though H 2 is discarded, truncated spectrum methodologies will often try to incorporate the effects of H 2 in some effective way. In these terms, we propose to keep the dimension of H 1 small. We pair this choice of H 1 with a Krylov subspace iterative approach able to take into account the effects of H 2 . This iterative approach can be taken to arbitrarily high order and so offers the ability to compute quantities to arbitrary precision. In many cases it also offers the advantage of not needing an explicit UV cutoff. To compute the matrix elements that arise in the Krylov iterations, we employ a Feynman diagrammatic representation that is then evaluated with Monte Carlo techniques. Each order of the Krylov iteration is variational and is guaranteed to improve upon the previous iteration. The first Krylov iteration is akin to the next-to-leading order approach of Elias-Miró [NLO renormalization in the Hamiltonian truncation, ]. To demonstrate this approach, we focus on the ( 1 + 1 d )-dimensional ϕ 4 model and compute the bulk energy and mass gaps in both the Z 2 -broken and unbroken sectors. We estimate the critical ϕ 4 coupling in the broken phase to be g c = 0.2645 ± 0.002 . Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024

Physics↗
DOE OSTI2021

Ethylene oxidation on unpromoted silver catalysts: Reaction pathway and selectivity analysis using DFT calculations

Chemical conversions in catalytic partial oxidation processes of light hydrocarbons are responsible for the production of numerous industrial chemicals, plastics, and intermediates. These processes are relatively expensive to perform, and are typically operated at high thermodynamic inefficiency, so the development of novel, highly efficient catalysts would prove to be very cost effective. Herein, our study focused on surface catalytic mechanisms of the ethylene oxide (EO) formation process. Periodic plane-wave Density Functional Theory (DFT) methods were used to analyze related reaction mechanisms on the Ag(111) surface facet with low coverage. Energetic changes of related species and pathways were calculated. Key surface species are identified to suggest the factors for the observed selectivity during EO formation. Our results are consistent with previous kinetic modeling efforts in the literature which did not employ DFT analysis. Lastly, our study demonstrates how fundamental theoretical investigations and multi-scale modeling techniques are currently impacting the advancement of rational catalyst design and microkinetic modeling techniques in the light hydrocarbon processing industry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Characterization and Amelioration of Filtration Difficulties Encountered in Metabolomic Studies of Clostridium thermocellum at Elevated Sugar Concentrations

Clostridium thermocellum , a promising candidate for consolidated bioprocessing, has been subjected to numerous engineering strategies for enhanced bioethanol production. Measurements of intracellular metabolites at substrate concentrations high enough (>50 g/L) to allow the production of industrially relevant titers of ethanol would inform efforts toward this end but have been difficult due to the production of a viscous substance that interferes with the filtration and quenching steps during metabolite extraction. To determine whether this problem is unique to C. thermocellum , we performed filtration experiments with other organisms that have been engineered for high-titer ethanol production, including Escherichia coli and Thermoanaerobacterium saccharolyticum . Here, we addressed the problem through a series of improvements, including active pH control (to reduce problems with viscosity), investigation of different filter materials and pore sizes (to increase the filtration capacity), and correction for extracellular metabolite concentrations, and we developed a technique for more accurate intracellular metabolite measurements at elevated substrate concentrations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

GeN-ROM—An OpenFOAM®-based multiphysics reduced-order modeling framework for the analysis of Molten Salt Reactors

This work presents a projection-based multiphysics Model Order Reduction (MOR) framework for the analysis of nuclear systems and its application to parametric simulations of Molten Salt Reactors (MSR). The framework, named GeN-ROM, is developed using OpenFOAM® and employs a Proper Orthogonal Decomposition aided Reduced-Basis technique (POD-RB). It can be used to reduce steady-state and transient multiphysics problems involving parametric fluid dynamics, heat exchange, and neutronics phenomena. For the treatment of structural elements in the hydraulic systems, a porous medium approach has been adopted. The reduction process is data-driven and snapshot information is extracted via POD to learn the solution manifold and to build global spatial basis functions. At the data collection phase, GeN-ROM makes use of the solvers available in GeN-Foam, a similarly OpenFOAM®-based multiphysics framework developed for the analysis of nuclear reactors. The global bases are used both to approximate the solution fields and to project the full-order equations onto lower-dimensional subspaces, thus considerably reducing the number of unknowns in a numerical system. This reduction leads to significant computational speedups, which is ideal for multi-query applications such as uncertainty quantification or design optimization. The developed tool has been tested using a 2D multiphysics model of the Molten Salt Fast Reactor (MSFR) with steady-state and transient scenarios, with speedups on the order of 10 – 10 5 .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Sneezing and asymptomatic virus transmission

The novel coronavirus disease (COVID-19) spread pattern continues to show that geographical barriers alone cannot contain a virus. Asymptomatic carriers play a critical role in the nature of this virus quickly escalating into a global pandemic. Asymptomatic carriers may transmit the virus unintentionally through sporadic sneezing. A novel Computational Fluid Dynamics (CFD) approach has been proposed with a realistic modeling of a human sneeze achieved by the combination of state-of-the-art experimental and numerical methods. This modeling approach may be suitable for future engineering analyses aimed at reshaping public spaces and common areas, with the main objective to accurately predict the spread of aerosol and droplets that may contain pathogens. This study shows that the biomechanics of a human sneeze, including complex muscle contractions and relaxations, can be accurately modeled by the angular head motion and the dynamic pressure response during sneezing. These have been considered as the human factors and were implemented in the CFD simulation by imposing a momentum source term to the coupled Eulerian–Lagrangian momentum equations. The momentum source was modeled by the measured dynamic pressure response in conjunction with the angular head motion. This approach eliminated the need to create an ad hoc set of inlet boundary conditions. With this proposed technique, it is easier to add multiple fixed and/or moving sources of sneezes in complex computational domains. Additionally, extensive sensitivity analyses based on different environmental conditions were performed, and their impact was described in terms of potential virus spread.

42 ENGINEERING↗
DOE OSTI2022

Computational Modeling of Multi-Pass Rolling Parameters Effect on Resulting Fuel Foil Shape

A focus of the U.S. Department of Energy is to improve production yield and reduce the cost of Low Enriched Uranium (LEU)-molybdenum alloy (U-10Mo) monolithic fuel plates that will be replacing High Enriched Uranium (HEU) oxide dispersion fuels used currently in the United States High Performance Research Reactors (USHPRR). One area of improvement is lowering the high transverse waviness and longitudinal waviness currently present within rolled foils prior to cladding to produce fuel plates. Traditional rolling manufacturing techniques for other metal foils use winders to pull and straighten the foil as it is rolled back and forth to the final thickness. This approach cannot be used to roll thin U-10Mo foils (0.008-0.025” thick) because only small castings can be rolled due to nuclear criticality safety concerns. As a result, the fuel foils are too short (1 m in length) to use traditional winders. Therefore, it is crucial to identify other rolling parameters (i.e., roller friction, axial tension load, roller diameter, and roll pass reduction percent) that might reduce transverse waviness and longitudinal waviness in the rolled fuel foil and develop a high-yield, low-cost multi-pass rolling manufacturing process. This report documents a systematic finite element modeling study to investigate the effects of numerous rolling parameters to reduce resulting transverse waviness and longitudinal waviness in the fuel foil during multi-pass rolling of U-10Mo foils. The rolling of a U-10Mo plate with initial dimensions of 1”x1”x 0.048” is modeled using Abaqus CAE. This rolling is modeled to undergo eight 20% reduction roll passes to a final fuel foil thickness of 0.01”. The elastic-plastic constitutive model of the U-10Mo alloy was input to the fuel foil rolling model. The rollers were modeled as rigid bodies. A comparison of rolling friction coefficients of 0.3 and 0.7 over a wide range of applied axial tension loads were investigated in order to evaluate the effect of using a lubricant during rolling. The effect of roller diameter on the resulting transverse waviness and longitudinal waviness of the fuel foil over a wide range of axial tension loads were also investigated by modeling rollers 7/8” and 3.75” in diameter. The results of this systematic finite element method study will aid manufacturers in producing low transverse waviness and reduced longitudinal waviness in U-10Mo fuel foils.

U-10Mo, FEA, Rolling, Residual Stress, Fuel Foil↗
DOE OSTI2021

Using AI to build a hydrobiogeochemical soil model

Soil water content is a function of inputs from precipitation and outputs via evaporation, transpiration, lateral flow, and vertical percolation, and is sensitive to biogeochemical processes. As such, soils serve as an ideal integrator of atmospheric, hydrological, and biogeochemical processes affecting the water cycle. In addition, soil water retention capacity, infiltration rates, and hydraulic conductivity can buffer or exacerbate the effects of extreme precipitation events (e.g., flooding, runoff, subsurface transport, erosion, greenhouse gas emissions) and mitigate the impact of droughts and heat waves on land systems (e.g., fire, crop failure). However, integrating water cycle measurements spanning different land atmosphere compartments across scales is a fundamental barrier for numerical model predictability. A significant challenge is that each domain (soil, hydrology, biology, and atmosphere) typically collects different sets of data at different temporal and spatial frequencies/scales, and even different dimensionalities (2D vs 3D). To implement soil as an integrator of the water cycle in land models, we suggest that novel machine learning (ML) tools can be developed to effectively simulate complex landscapes across various domains and scales, extended to regions with sparse or no data. The ultimate goals are to improve predictive understanding of land-atmosphere interactions and to extend the predictability of current Earth System Models (ESMs) through better integration of hydrological and biogeochemical data. We envision a framework in which: (1) ML-aided data reconstructions enable the merger of data sources into a unified geospatial product; (2) automated detection techniques are used to improve the knowledge of complex soil processes and interactions; and (3) this knowledge is leveraged and incorporated into models through AI-based emulators to distinctly connect the land and atmospheric compartments of the water cycle in models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evaluation of Tungsten—Steel Solid-State Bonding: Options and the Role of CALPHAD to Screen Diffusion Bonding Interlayers

Critical aspects of innovative design in engineering disciplines like infrastructure, transportation, and medical applications require the joining of dissimilar materials. This study investigates the literature on solid-state bonding techniques, with a particular focus on diffusion bonding, as an effective method for establishing engineering bonds. Welding and brazing, while widely used, may pose challenges when joining materials with large differences in melting temperature and can lead to mechanical property degradation. In contrast, diffusion bonding offers a lower temperature process that relies on solid-state interactions to develop bond strength. The joining of tungsten and steel, especially for fusion reactors, presents a unique challenge due to the significant disparity in melting temperatures and the propensity to form brittle intermetallics. Here, diffusion characteristics of tungsten–steel interfaces are examined and the influence of bonding parameters on mechanical properties are investigated. Additionally, CALPHAD modeling is employed to explore joining parameters, thermal stability, and diffusion kinetics. The insights from this research can be extended to join numerous dissimilar materials for specific applications such as aerospace, automobile industry, power plants, etc., enabling advanced and robust design with high efficiency.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Advanced absorber heat integration via heat exchange packings

A rate-based model of an absorption column was developed and used to analyze several intercooling strategies utilizing “heat exchange packings.” These packings are capable of removing heat from the column and transferring it to a cooling fluid within the packing. For absorption of CO 2 into aqueous monoethanolamine under industrial conditions, intercooling via heat exchange packings placed along 10–20% of the column could reduce the column height by ~15%. The height of these columns was close to the minimum theoretical value, calculated by numerically optimizing the temperature profile. Effective intercooling could also be achieved by using the cool, rich solvent as the cooling fluid. This reduces the cooling load and facilitates recovery of waste heat. Heat exchange packings could also be used to redistribute heat within the column, reducing the column height with no net cooling load. However, this approach requires larger heat transfer coefficients than have been experimentally observed.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2021

Precambrian Crystalline Basement Properties From Pressure History Matching and Implications for Induced Seismicity in the US Midcontinent

Injection-induced seismicity across the US midcontinent has almost exclusively occurred in the crystalline basement that underlies the Arbuckle Group aquifer and its equivalents, the primary wastewater disposal zone in this region. However, the properties of the basement are not well known. Newly compiled data, from Class I wells in Kansas, provide a unique record of pressures in the Arbuckle and an opportunity to constrain the reservoir-scale properties of the basement such as permeability, diffusivity, and specific storage. Constraints on these parameters are critical for modeling fluid flow and pressures across the entire Arbuckle-basement system, and are necessary for accurate evaluation and prediction of injection-induced earthquakes. Here, we present a detailed, three-dimensional geological and pressure history-matched numerical model for the Arbuckle and basement, based on data from >400 wells covering a large region in south-central Kansas, where injection-induced seismicity has been concentrated since 2014. Simulations of dynamic data from 319 wells indicate that Arbuckle pressures have increased by 1.1 MPa in high injection rate areas and an overpressure of <0.1 MPa may be the cause of seismicity in the basement. Pressure-history matching also yields the likely range in porosity (0.3%–7%), permeability (0.1–0.7 mD), and diffusivity (0.004–0.07 m2 /s) for the basement. The resulting estimates suggest reservoir-scale properties of the basement are enhanced by faults and fractures. Importantly, the diffusivities determined in this study are lower than estimates derived from Kansas earthquake triggering fronts, and suggest that such seismicity-based techniques may have limitations, particularly where spacetime patterns between injection and seismicity are complex.

58 GEOSCIENCES↗
DOE OSTI2022

Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning

Abstract We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC–AE) has been shown to capture nonlinear solution manifolds but fails to perform adequately when linear subspace approaches such as proper orthogonal decomposition (POD) would be optimal. Besides, most DL-ROM models rely on convolutional layers, which might limit its application to only a structured mesh. The proposed framework in this study relies on the combination of an autoencoder (AE) and Barlow Twins (BT) self-supervised learning, where BT maximizes the information content of the embedding with the latent space through a joint embedding architecture. Through a series of benchmark problems of natural convection in porous media, BT–AE performs better than the previous DL-ROM framework by providing comparable results to POD-based approaches for problems where the solution lies within a linear subspace as well as DL-ROM autoencoder-based techniques where the solution lies on a nonlinear manifold; consequently, bridges the gap between linear and nonlinear reduced manifolds. We illustrate that a proficient construction of the latent space is key to achieving these results, enabling us to map these latent spaces using regression models. The proposed framework achieves a relative error of 2% on average and 12% in the worst-case scenario (i.e., the training data is small, but the parameter space is large.). We also show that our framework provides a speed-up of $$7 \times 10^{6}$$ 7 × 10 6 times, in the best case, and $$7 \times 10^{3}$$ 7 × 10 3 times on average compared to a finite element solver. Furthermore, this BT–AE framework can operate on unstructured meshes, which provides flexibility in its application to standard numerical solvers, on-site measurements, experimental data, or a combination of these sources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Benchmarking NIMROD continuum kinetic formulations through the steady-state poloidal flow

In this work, continuum kinetic formulations are employed as a mechanism to include closure physics in an extended magnetohydrodynamics model. Two continuum kinetic approaches have been implemented in the plasma fluid code NIMROD [Sovinec et al., “Nonlinear magnetohydrodynamics with high-order finite elements,” J. Comput. Phys. 195, 355 (2004)] including a Chapman–Enskog-like (CEL) formulation and a more conventional df approach. Ion kinetic closure schemes are employed to describe the neoclassical flow properties in axisymmetric toroidal geometry. In particular, predictions for steady-state values of poloidal flow profiles in tokamak geometry are provided using both the df formulation and two different solution techniques for the CEL approach. These results are benchmarked against analytic theory predictions as well as results from the drift kinetic code DK4D. The continuum kinetic formulations employed here show agreement with both the analytic theory and DK4D results, and offer a novel velocity space representation involving higher-order finite elements in pitch angle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Quantum error mitigation by layerwise Richardson extrapolation

A widely used method for mitigating errors in noisy quantum computers is Richardson extrapolation, a technique in which the overall effect of noise on the estimation of quantum expectation values is captured by a single parameter that, after being scaled to larger values, is eventually extrapolated to the zero-noise limit. We generalize this approach by introducing layerwise Richardson extrapolation (LRE), an error mitigation protocol in which the noise of different individual layers (or larger chunks of the circuit) is amplified and the associated expectation values are linearly combined to estimate the zero-noise limit. The coefficients of the linear combination are analytically obtained from the theory of multivariate Lagrange interpolation. LRE leverages the flexible configurational space of layerwise unitary folding, allowing for a more nuanced mitigation of errors by treating the noise level of each layer of the quantum circuit as an independent variable. Furthermore, we provide numerical simulations demonstrating scenarios where LRE achieves superior performance compared to traditional (single-variable) Richardson extrapolation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation

The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world’s largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A geometric framework for momentum-based optimizers for low-rank training

Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers such as heavy ball momentum methods or Adam. In this work, we identify and analyze potential difficulties that these training methods encounter when used to train low-rank parameterizations of weights. In particular, we show that classical momentum methods can struggle to converge to a local optimum due to the geometry of the underlying optimization landscape. To address this, we introduce novel training strategies derived from dynamical low-rank approximation, which explicitly account for the underlying geometric structure. Our approach leverages and combines tools from dynamical low-rank approximation and momentum-based optimization to design optimizers that respect the intrinsic geometry of the parameter space. We validate our methods through numerical experiments, demonstrating faster convergence, and stronger validation metrics at given parameter budgets.

Schotthoefer, Steffen [ORNL] (ORCID:00000002156965↗
DOE OSTI2022

Nonresonant particle acceleration in strong turbulence: Comparison to kinetic and MHD simulations

Collisionless, magnetized turbulence offers a promising framework for the generation of nonthermal high-energy particles in various astrophysical sites. Yet, the detailed mechanism that governs particle acceleration has remained subject to debate. By means of 2D and 3D particle-in-cell, as well as 3D (incompressible) magnetohydrodynamic (MHD) simulations, we test here a recent model of nonresonant particle acceleration in strongly magnetized turbulence, which ascribes the energization of particles to their continuous interaction with the random velocity flow of the turbulence, in the spirit of the original Fermi model. To do so, we compare, for a large number of particles that were tracked in the simulations, the predicted and the observed histories of particles momenta. The predicted history is that derived from the model, after extracting from the simulations, at each point along the particle trajectory, the three force terms that control acceleration: the acceleration of the field line velocity projected along the field line direction, its shear projected along the same direction, and its transverse compressive part. Overall, we find a clear correlation between the model predictions and the numerical experiments, indicating that this nonresonant model can successfully account for the bulk of particle energization through Fermi-type processes in strongly magnetized turbulence. Additionally we also observe that the parallel shear contribution tends to dominate the physics of energization in the particle-in-cell simulations, while in the magnetohydrodynamic incompressible simulation, both the parallel shear and the transverse compressive term provide about equal contributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

The impact of optical measurement techniques on measured aerosol particle size distributions

Ambient aerosol particle size distributions measured by the Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) at various sites around the world exhibit modes at optical diameters near 600 nm and 850 nm. These modes are not present in concurrent measurements with the Grimm 11-D Optical Particle Counter (OPC). Here, in this study, we argue that these modes result from the optical measurement technique itself, and we explain why they appear in measurements by the UHSAS but not in those by the Grimm OPC. We construct computer models of the UHSAS and Grimm (“digital UHSAS” and “digital Grimm”) and use these to investigate the size distribution that would result from measurements of artificial aerosol particle size distributions that do not contain modes. The appearance of modes for the structureless incoming size distributions sampled by the digital UHSAS is explained by the nonlinear behavior of partial scattering cross sections of uniform spherical particles as a function of their diameter. The absence of modes in the digital Grimm is explained by the coarser size resolution of that instrument. Detailed analysis of the relationship between optical and geometric diameters for uniform spherical particles reveals two important results. First, these diameters generally have different numerical values for the same particle, and second, the relationship is nonlinear; thus, widths of size bins in terms of optical diameter differ from those in geometric diameter. These results explain the modes observed in the ambient size distributions and highlight concerns with attempts to create a merged size distribution by combining measurements from different instruments.

54 ENVIRONMENTAL SCIENCES↗