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DOE OSTI2021

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Single-particle dynamics of microbunching

The mechanism of steady-state microbunching (SSMB) has been proposed [D. F. Ratner and A. W. Chao, Phys. Rev. Lett. 105, 154801 (2010)] to generate high-power coherent radiation at a high repetition rate or in continuous-wave mode using electron storage rings. In this paper, the related single-particle dynamics are theoretically and numerically studied, and important results are presented. The investigated effects are longitudinal quantum radiation excitation, nonlinear momentum compaction, and linear and nonlinear coupling of the transverse and longitudinal motion. Although this analysis is oriented toward SSMB, some of the analyzed effects are also crucial in cases such as coherent harmonic generation, bunch slicing, bunch compression, free-electron laser beam transport lines, and quasi-isochronous rings, which involve precise longitudinal phase-space manipulations.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Municipality of Anchorage Household Travel Survey

The 2002 Household Travel Survey for the municipality of Anchorage, Alaska, collected demographic, socioeconomic, and travel information about households and persons (age five and older) on an assigned, 24-hour travel period. The main objective of the study, conducted by NuStats, was to improve the transportation system. 2,035 households were recruited to participate in the study. Of these, 1,293 completed travel logs depicting detailed data on driving habits, such as purpose of the trips, time of the data, and mode of transportation—spanning from April 1, 2002, to May 17, 2002. This dataset is part of the Metropolitan Travel Survey Archive, which includes travel surveys from numerous public agencies across the United States and is archived by the Transportation Secure Data Center to ensure their continued public availability.

1Hz data↗

DOE OSTI2026

2001 Atlanta Household Travel Survey

The 2001 Atlanta Household Travel Survey collected demographic, socioeconomic, and travel information on work and non-work travel behavior for a 48-hour travel period. The study was conducted on behalf of the Atlanta Regional Commission, and it is an essential element in the transportation planning and modeling efforts for the 13-county Atlanta region. The main objective of the study was to produce data that could be used to develop and calibrate travel demand models for use in travel forecasting, land use planning, and air quality planning to improve the transportation system. The second component in the survey was the deployment of an electronic travel diary with person-based GPS and an accelerometer to collect health and activity information. Travel data includes trip generation, trip distribution, and modal choice. The survey recruited a total of 12,184 households to participate in the study. Of these, 8,069 households (66%) completed travel. The 8,069 households, when weighted, represent 21,323 persons, 14,449 vehicles, and 126,127 places visited from April 2001 through April 2002. This dataset is part of the Metropolitan Travel Survey Archive, which includes travel surveys from numerous public agencies across the United States and is archived by the Transportation Secure Data Center to ensure their continued public availability.

1Hz data↗

DOE OSTI2024

Research Reactors Division Infrastructure Investment Plan for the High Flux Isotope Reactor

The High Flux Isotope Reactor (HFIR) is a unique national asset. Operational for nearly 60 years, continued investment into the aging infrastructure is necessary to ensure operation for another 6 decades. Additionally, growing missions require HFIR as well as important upgrades. Consequently, carefully integrated planning is required to ensure that infrastructure investments are timely executed to ensure long-term, reliable operation of HFIR. Concerns about challenges to the operational reliability of HFIR resulted in a recommendation from the 2023 Operations Review by the US Department of Energy (DOE) Office of Basic Energy Sciences that a HFIR management strategy be developed to address the infrastructure needs. This report defines the investment needs, which are evolving as new upgrade efforts are better defined. HFIR is part of the three-source strategy within the Neutron Sciences Directorate (NScD) and contributes to the five strategic science areas outlined in the NScD 10 Year Strategic Science Plan: quantum materials, soft matter, materials and engineering, chemistry, and biosciences. Fundamental to this strategy are three core values: operational excellence, responsible stewardship, and servant leadership. These values guide our mission of safe and reliable operation of the reactor and require a strong and just nuclear safety culture, a solemn respect for responsible care of the facility, good workforce development, robust procedures and processes, an effective communication strategy, world-class asset management, a determined customer focus, and a commitment to protecting the environment, the safety and health of the public and our people, and the quality of work performed within our facility. These principles are all essential to operate HFIR at a world-class level. The Research Reactors Division (RRD) will lead a new era of neutron science and isotope production at HFIR through responsible and purposeful leadership and unwavering support of the science community. The approach outlined in this plan highlights the direction leadership is taking to ensure that HFIR is ready to support the science challenges and national needs of the future and that the United States maintains world leadership in neutron sciences. The plan is in alignment with the DOE’s desire to continue operating HFIR and with the NScD strategic science goals for the future. HFIR is an aging facility with numerous infrastructure challenges and needs. It has an aging workforce in relation to the general population of Oak Ridge National Laboratory (ORNL), with many expected retirements over the next 5–10 years. With an increase in work scope caused by changing national priorities and science goals, several critical hires have been identified. To manage HFIR’s infrastructure needs, a prioritized list of equipment upgrades has been identified along with an analysis of future staffing requirements. A desire to operate HFIR at eight cycles per year will necessarily require some significant changes to procedures and processes currently in place as well as targeted staffing additions. Many of the equipment upgrades identified in this plan will significantly increase the reliability of the plant, thus contributing to the effort to reach the goal of safely operating eight cycles per year. A plan to attain eight-cycle operation is being prepared in parallel with the activities identified in this plan, although the actions identified to satisfy both plans will overlap. This plan identifies new infrastructure needs—for both plant equipment and staffing—thus necessitating formulation of future budget requests to fund the increased work scope and improvement activities. Some activities are currently being scheduled with the expectation that funding will be received. Any delays to funding or reductions of funding from the identified cost estimations will directly and negatively affect the plan’s implementation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2025

A detailed study of pre-heating effects in electron beam melting powder bed fusion process

Metal-based additive manufacturing processes, such as powder bed fusion with electron beam (PBF-EB) process, also referred to as electron beam melting (EBM), can produce high-density parts with minimal residual stresses due to the uniform and coherent preheating of the powder bed. However, understanding and controlling the multiple stages of preheating is required to enable the production of high-quality, consistent parts of various materials. This work presents a large-scale, multi-layer, three-dimensional numerical analysis focused on studying the preheating stages for predicting thermal history during the PBF-EB process. The model follows a continuous multi-stage cyclic process, that incorporates all the main stages of the PBF-EB process for 316 L stainless steel. This includes the gradual deposition of a new powder layer, the first and second preheating levels of the powder bed, and the energy deposition during melting (excluding the actual melt-pool behavior simulation). The model employs an adaptive time-scaling approach that automatically adjusts the energy deposition for each solution time-increment. This allows for localized changes in time-resolution over an otherwise computationally expensive multi-layer procedure. The material property variations are also taken into account, with an emphasis on the subtle irreversible changes in powder effective thermal conductivity after the two requisite preheating stages of the powder bed. This effect is studied using simplified conductivity models from the literature for partially sintered powder, validated by a dedicated experiment and numerical simulation. The large-scale model is then used to estimate the actual temperatures during first and second preheating levels for 316 L steel, which is not yet fully supported commercially for PBF-EB. Model predictions are corroborated by experiments, using and analyzing IR images, taken at the completion of each layer by the machine’s built-in infrared camera. The current model also incorporates a qualitative assessment for the effects of conductivity change during pre-heating, as well as evaluates the applicability of the time-scaling approach.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Phase field-volumetric lattice Boltzmann model of ion uptake in porous nuclear waste form materials under continuous flow

The flow field within the mesopores of sorbent particles plays a crucial role in radionuclide diffusion and ion uptake kinetics, thus, impacting the overall performance of porous nuclear waste form materials. To fundamentally understand the influence of microstructures and material properties on the radionuclide absorption and retention processes requires a coupled multi-physics model that considers the advection and diffusion within the flow field, the reaction at liquid-solid interfaces, and finally, the solid-state diffusion within a complex nanoporous medium. Here, this study employs the volumetric lattice Boltzmann method (VLBM) to accurately and efficiently calculate the steady state velocity field inside the mesopores of sorbent particles. The obtained velocity field is then utilized to calculate the advection of ions in the steady flow. A phase field (PF) model of ion uptake is used to describe the reaction occurring at the solid-liquid interface and diffusion inside the porous medium. The integrated PF-VLBM model is verified in terms of the mass conservation and numerical efficiency and validated qualitatively with experimental observation data. Then, it is applied to study the influence of thermodynamic and kinetic properties, as well as flow field conditions on the ion uptake kinetics. The numerical results demonstrate that the ion uptake kinetics in porous particles has three distinct stages, which is in agreement with the observations in continuous flow experiments. In the first stage, the kinetics is predominantly controlled by the flow field and ion diffusivity in the liquid phase. The kinetics in the second stage is primarily governed by ion diffusivity in the solid phase. In the third stage the system reaches a dynamic equilibrium with a net zero uptake flux at the interface. It is also found that porous structures significantly affect the efficiency and capacity of ion uptake. The simulation results can help to understand the physics behind the observed ion uptake kinetics in experiments and to facilitate the development of constitutive equations that can account for heterogeneous microstructures in engineering performance codes.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A variational multiscale immersed meshfree method for heterogeneous materials

Abstract We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition is imposed by a volumetric constraint, which avoids a tedious contour integral for complex material geometry. The proposed immersed approach is formulated under a variational multiscale based formulation, termed the variational multiscale immersed method (VMIM). Under this framework, the solution approximation on either the foreground or the background can be decoupled into coarse-scale and fine-scale in the variational equations, where the fine-scale approximation represents a correction to the residual of the coarse-scale equations. The resulting fine-scale solution leads to a residual-based stabilization in the VMIM discrete equations. The employment of reproducing kernel (RK) approximation for the coarse- and fine-scale variables allows arbitrary order of continuity in the approximation, which is particularly advantageous for modeling heterogeneous materials. The effectiveness of VMIM is demonstrated with several numerical examples, showing accuracy, stability, and discretization efficiency of the proposed method.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A pseudospectral implicit particle-in-cell method with exact energy and charge conservation

The standard particle-in-cell (PIC) method employs explicit finite-difference (FD) methods (e.g. the leap-frog scheme) for both spatial and temporal integrations. Here, we employ a pseudospectral method for solving the Poisson equation and a fully implicit time integration to achieve exact energy conservation. The advantage of a pseudospectral field solver is its spectral accuracy in solving field solutions. Earlier studies of implicit time integration of PIC FD equations can enforce exact energy exchange between field and particles, resulting in exact energy-conserving schemes. Here, we prove that the exact energy conservation property can be carried over to the pseudospectral scheme. Simultaneously, we provide a solution to ensure a pseudospectral charge continuity equation. We demonstrate the new scheme in a 2D electrostatic PIC code. In conclusion, theoretical results are confirmed via numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The future of computing beyond Moore’s Law

Moore’s Law is a techno-economic model that has enabled the information technology industry to double the performance and functionality of digital electronics roughly every 2 years within a fixed cost, power and area. Advances in silicon lithography have enabled this exponential miniaturization of electronics, but, as transistors reach atomic scale and fabrication costs continue to rise, the classical technological driver that has underpinned Moore’s Law for 50 years is failing and is anticipated to flatten by 2025. Here, this article provides an updated view of what a post-exascale system will look like and the challenges ahead, based on our most recent understanding of technology roadmaps. It also discusses the tapering of historical improvements, and how it affects options available to continue scaling of successors to the first exascale machine. Lastly, this article covers the many different opportunities and strategies available to continue computing performance improvements in the absence of historical technology drivers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Leveraging Multitime Hamilton–Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional quantity, HJ PDEs can be extended to the multi-time case. In this paper, we establish a novel theoretical connection between specific optimization problems arising in machine learning and the multi-time Hopf formula, which corresponds to a representation of the solution to certain multi-time HJ PDEs. Through this connection, we increase the interpretability of the training process of certain machine learning applications by showing that when we solve these learning problems, we also solve a multi-time HJ PDE and, by extension, its corresponding optimal control problem. As a first exploration of this connection, we develop the relation between the regularized linear regression problem and the Linear Quadratic Regulator (LQR). We then leverage our theoretical connection to adapt standard LQR solvers (namely, those based on the Riccati ordinary differential equations) to design new training approaches for machine learning. Lastly, we provide some numerical examples that demonstrate the versatility and possible computational advantages of our Riccati-based approach in the context of continual learning, post-training calibration, transfer learning, and sparse dynamics identification.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

CTH v.13.0

SAND2023-06647O The latest version of the CTH suite of computer codes is a flexible software system designed to treat a wide range of shock wave propagation and material motion phenomena in 1-D, 2-D, or 3-D. CTH has models suitable for most conditions encountered in shock physics including material strength, fracture, distended materials, high explosives, and a variety of boundary conditions. Finite-volume analogs of the Lagrangian equations of momentum and energy conservation are employed with continuous rezoning to construct Eulerian differencing. Adaptive mesh refinement is available for maximizing resolution in regions of interest. Full Lagrangian numerical methods are available for mechanical or structural response.

Schumacher, Shane↗

DOE OSTI2024

Single-shot Quantum Signal Processing Interferometry

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Physics↗

DOE OSTI2020

Calculation Of The First Moment Of Energy Using D-T Reactivity Formalisms Under The Maxwell-Boltzmann Distribution--Part II

Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of a nuclear fusion formalism is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium- Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hal reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell-Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. This report continues the step toward building understanding of nuclear fusion reactivity formalisms. It is part of a series of reports with the same goal, [5-10] and is the continuation of the Part I paper for defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, <$E$>, with the fusion cross-section, fusion reactivity and its derivative with ion-temperature. In Part I, three variants of the first moment <$E$> were analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment from Brysk. In Part II, attention is given to the definition of <$K$>, originally described as a ratio of moments from Brysk, and its relationship to the first moment definitions from Part I. One measure of the progress made in these documents is the identification that Brysk’s ratio of the second moment to the first moment ratio, <$K$>, does not correspond to his provided solution of the first moment of energy. Another measure of (our) progress from this work is the comparison of first moment variants. That comparison includes confirming the importance of cross sections defined in terms of energy. The analytical relationships we have developed among important physics quantities are useful tools in validation and verification (V&V). For example, we can calculate the kinetic energy as a mean or as a first moment, or as a function of the first moment. These analytically-determined values can be compared directly with numerically-determined values, supplied to the authors, representing <$E$>.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

An extrapolation method for strain ranges and hold times in developing the EPP+SMT creep-fatigue design curves for Alloy 617

Experimental and numerical studies in developing the integrated Elastic–Perfectly Plastic (EPP) plus Simplified Model Test (SMT) design methodology, referred to as the EPP+SMT method, continued in FY2022. This report focuses on the methods for extrapolating the EPP+SMT creep-fatigue (CF) design curves at long hold times and low strain ranges. In this study, the available CF failure data on Alloy 617 at 950°C were analyzed to determine a set of CF failure criteria. At very low strain ranges and long hold times, CF failure data are not accessible by experiments because of the extraordinarily long test durations and the inability of the test machines to accurately control these small strain ranges. A CF experimental approach with the concept of block-strain range CF testing protocol was developed. Tests using this protocol were conducted to generate the needed information for calibrating material parameters of the numerical material models. The Time Fraction based method and Dissipated Energy method were used to extrapolate the CF life curves to low strain ranges and long hold times. Based on the new experimental approach and CF life prediction methods, the CF life curves with various hold times were developed for Alloy 617 at 950°C. In addition, an experiment was designed and is being performed to verify the predicted CF curves at 950°C. The extrapolation procedure will be applied at lower temperatures to complete the development of the EPP+SMT CF design curves for Alloy 617 in F2023.

36 MATERIALS SCIENCE↗