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DOE OSTI2019

Estimating Code Biases for Criticality Safety Applications with Few Relevant Benchmarks

Criticality safety analyses rely on the availability of relevant benchmark experiments to determine justifiable margins of subcriticality. When a target application lacks neutronically similar benchmark experiments, validation studies must provide justification to the regulator that the impact of modeling and simulation limitations is well understood for the application and often must provide additional subcritical margin to ensure safe operating conditions. This study estimated the computational bias in the critical eigenvalue for several criticality safety applications supported by only a few relevant benchmark experiments. The accuracy of the following three methods for predicting computational biases was evaluated: the Upper Subcritical Limit STATisticS (USLSTATS) trending analysis method; the Whisper nonparametric method; and TSURFER, which is based on the generalized linear least-squares technique. Here, these methods were also applied to estimate computational biases and recommended upper subcriticality limits for several critical experiments with known biases and for several cases from a blind benchmark study. The methods are evaluated based on both the accuracy of their predicted computation bias and upper subcriticality limit estimates, as well as on the consistency of the methods’ estimates, as the model parameters, covariance data libraries, and set of available benchmark data were varied. Data assimilation methods typically have not been used for criticality safety licensing activities, and this study explores a methodology to address concerns regarding the reliability of such methods in criticality safety bias prediction applications.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2021

Recent Updates in ETOE-2 and MC 2 -3

The MC 2 -3 code is a multigroup cross section generation code for fast reactor applications, developed by Argonne National Laboratory (ANL) under the DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. In this work, first, the cross section libraries for ENDF/B-VII.1 and ENDF/B-VIII.0 data were generated using the updated ETOE-2 code. Preliminary verification and validation tests of the ENDF/B-VII.1 MC 2 -3 library were performed with the selected fast reactor benchmark problems. Processing and verifying the libraries suggested that significant efforts would be required for thoroughly verifying the ENDF/B-VII.1 MC 2 -3 library and successfully processing the ENDF/B-VIII.0 MC 2 -3 library. Secondly, the cross section generation capability of MC 2 -3 was updated with the intermediate group lattice calculation and the equivalent Dancoff-factor cell (EDC) method to significantly improve the performance of a twodimensional assembly calculation using the method of characteristics (MOC). This effort was made useful in implementing and verifying the EDC method in the Griffin cross section API. Finally, we analyzed a SFR problem, for which unusually large deviations in core eigenvalues from Monte Carlo solutions were reported, by generating multigroup cross sections with MC 2 -3, performing core calculations with DIF3D-VARIANT, and analyzing cross section and eigenvalue results against Monte Carlo solutions. The analysis confirmed that the MC 2 -3/DIF3D solutions were in good agreement with Monte Carlo solutions, providing the correct process of accurately generating broad-group cross sections with MC 2 -3

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

TARDIS. I. A Constrained Reconstruction Approach to Modeling the z ~ 2.5 Cosmic Web Probed by Lyα Forest Tomography

Recent Lyα forest tomography measurements of the intergalactic medium (IGM) have revealed a wealth of cosmic structures at high redshift (z ~ 2.5). In this work, we present the Tomographic Absorption Reconstruction and Density Inference Scheme (TARDIS), a new chronocosmographic analysis tool for understanding the formation and evolution of these observed structures. Here, we use maximum likelihood techniques with a fast nonlinear gravitational model to reconstruct the initial density field of the observed regions. We find that TARDIS allows accurate reconstruction of smaller-scale structures than standard Wiener-filtering techniques. Applying this technique to mock Lyα forest data sets that simulate ongoing and future surveys such as CLAMATO, Subaru PFS, or the ELTs, we are able to infer the underlying matter density field at observed redshift and classify the cosmic web structures. We find good agreement with the underlying truth in both the characteristic eigenvalues and eigenvectors of the pseudo-deformation tensor, with the eigenvalues inferred from 30 m class telescopes correlated at r = 0.95 relative to the truth. As an output of this method, we are able to further evolve the inferred structures to late time (z = 0) and also track the trajectories of coeval z = 2.5 galaxies to their z = 0 cosmic web environments.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Solving the $k$-Sparse Eigenvalue Problem with Reinforcement Learning

We examine the possibility of using a reinforcement learning (RL) algorithm to solve large-scale eigenvalue problems in which the desired the eigenvector can be approximated by a sparse vector with at most k nonzero elements, where k is relatively small compare to the dimension of the matrix to be partially diagonalized. Here, this type of problem arises in applications in which the desired eigenvector exhibits localization properties and in large-scale eigenvalue computations in which the amount of computational resource is limited. When the positions of these nonzero elements can be determined, we can obtain the k-sparse approximation to the original problem by computing eigenvalues of a k × k submatrix extracted from k rows and columns of the original matrix. We review a previously developed greedy algorithm for incrementally probing the positions of the nonzero elements in a k-sparse approximate eigenvector and show that the greedy algorithm can be improved by using an RL method to refine the selection of k rows and columns of the original matrix. We describe how to represent states, actions, rewards and policies in an RL algorithm designed to solve the k-sparse eigenvalue problem and demonstrate the effectiveness of the RL algorithm on two examples originating from quantum many-body physics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Physics-constrained Deep Recurrent Neural Models of Building Thermal Dynamics

We develop physics-constrained and control-oriented predictive deep learning models for the thermal dynamics of a real-world commercial office building. The proposed method is based on the systematic encoding of physics-based prior knowledge into a structured recurrent neural architecture. Specifically, our model mimics the structure of the building thermal dynamics model and leverages penalty methods to model inequality constraints. Additionally, we use constrained matrix parameterization based on the Perron-Frobenius theorem to bound the eigenvalues of the learned network weights. We interpret the stable eigenvalues as dissipativeness of the learned building thermal model. We demonstrate the effectiveness of the proposed approach on a dataset obtained from an office building with $20$ thermal zones.

Building Energy, structured neural networks↗

DOE OSTI2018

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

SCALE capabilities for high temperature gas-cooled reactor analysis

The SCALE code system’s ability to address stochastic distributions of fuel particles within a graphite matrix has been revisited in both multigroup (MG) features and continuous-energy (CE) Monte Carlo methods. Furthermore, this paper describes current and emergent SCALE capabilities within the CSAS sequence to address double-heterogeneous systems and presents verification and validation studies of these methods and data. Good agreement was obtained for a high temperature gas-cooled reactor (HTGR) fuel pebble model between CSAS MG eigenvalue calculations and corresponding CE reference solutions. Code-to-code comparisons for this HTGR pebble model showed good agreement of CSAS-KENO and CSAS-Shift CE calculations and the Serpent and MCNP codes in terms of eigenvalues and reaction rate ratios. Validation studies based on two HTGR experiments resulted in good agreement between MG and CE results, as well as between experiment and calculation, although the level of agreement was significantly influenced by the applied ENDF/B nuclear data library.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Limits on Subcritical Reactivity Determination using Rossi-α and Related Methods

The subcritical reactivity, ρ, of a neutron multiplying system is of interest to many factions of the nuclear community. The subcritical reactivity in a nuclear system can be inferred from measurements of the prompt neutron decay constant, α. Near critical, the reactivity is linearly proportional with α, but the linearity between these quantities does not hold in systems with low multiplication or significantly above prompt critical. This work examines a large range of subcritical prompt neutron decay constant measurements on a thermal HEU metal system. This system is designed to mimic a solution system and to have the optimal H/ 235 U ratio to minimize the critical mass. The reactivity of these measurements varies between 0$\$$ and 70$\$$ below critical. In addition to experimental measurements on the thermal system, simulations are performed on both the thermal HEU system and a fast HEU metal system. Both the fast and thermal results are compared to baseline simulations performed using criticality eigenvalue (KCODE) mode in MCNP®6.2. These simulations are used for comparisons on the linearity between α and ρ. Prompt neutron decay constant measurements in this work are performed using the Rossi-α method. The measurements are taken using a 3 He neutron detection system and a Los Alamos National Laboratory designed list-mode data acquisition system. A specially designed computer program determines α from list-mode data. The α-eigenvalue, or α at delayed critical, for the thermal HEU system is -199:4±4:4 s -1 as measured during this work. The α-eigenvalue for the fast HEU system was previously measured to be -8:5 x 10 -5 s -1 . The results from the thermal HEU system study suggest that the relationship between ρ and α is linear when k eff > 0:80 based on the simulation results. The experimental results also agree with this result, but have less fidelity. No experimental results are available for the fast HEU system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

A posteriori superlinear convergence bounds for block conjugate gradient

In this paper, we extend to the block case the a posteriori bound showing superlinear convergence of the conjugate gradient method developed by van der Vorst and Vuik in [J. Comput. Applied Math., 48 (1993), pp. 327–341]. That is, we obtain similar bounds but now for the block conjugate gradient method. We also present a series of computational experiments, illustrating the validity of the bound developed here as well as the bound by Simoncini and Szyld from [SIAM Review, 47 (2005), pp. 247–272] using angles between subspaces. Using these bounds, we make some observations on the onset of superlinearity and how this onset depends on the eigenvalue distribution and the block size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

SIESTA-SIPs: Massively parallel spectrum-slicing eigensolver for an ab initio molecular dynamics package

Integration of Shift-and-Invert Parallel spectral transformation (SIPs) eigensolver (as implemented in the SLEPc library) into an ab initio molecular dynamics package, SIESTA, is described. The effectiveness of the code is demonstrated on applications to polyethylene chains, boron nitride sheets, and bulk water clusters. For problems with the same number of orbitals, the performance of the SLEPc eigensolver depends on the sparsity of the matrices involved, favoring reduced dimensional systems such as polyethylene or boron nitride sheets in comparison to bulk systems like water clusters. For all problems investigated, performance of SIESTA-SIPs exceeds the performance of SIESTA with default solver (ScaLAPACK) at the larger number of cores and the larger number of orbitals. A method that improves the load-balance with each iteration in the self-consistency cycle by exploiting the emerging knowledge of the eigenvalue spectrum is demonstrated

ab initio↗

DOE OSTI2019

Mixed structures of optical breather and rogue wave for a variable coefficient inhomogeneous fiber system

Breathers and rogue waves are two special types of soliton and play significant role in optical fibers. In this work, the mixed breather and rogue wave solution is constructed for a variable coefficient inhomogeneous fiber system via the Darboux transformation method. The impacts on the mixed wave of the first- and second-order group velocity dispersions (GVD), are discussed, respectively. The spectral eigenvalue parameter control is also studied. The pulse wave width, amplitude and wave density can be controlled by the variable GVD functions and spectral eigenvalue parameter. Especially, two types of rogue wave solutions can be derived from the mixed solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures

Quantum mechanical calculations for material modeling using Kohn–Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. Here, these calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn–Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh–Ritz projection step of the discretized Kohn–Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Analyzing Prospects for Quantum Advantage in Topological Data Analysis

Lloyd [Nat. Commun. , 10138 (2016)] were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets. Here, we propose, analyze, and optimize an improved quantum algorithm for topological data analysis (TDA) with reduced scaling, including a method for preparing Dicke states based on inequality testing, a more efficient amplitude estimation algorithm using Kaiser windows, and an optimal implementation of eigenvalue projectors based on Chebyshev polynomials. We compile our approach to a fault-tolerant gate set and estimate constant factors in the Toffoli complexity. Our analysis reveals that superquadratic quantum speedups are only possible for this problem when targeting a multiplicative error approximation and the Betti number grows asymptotically. Further, we propose a dequantization of the quantum TDA algorithm that shows that having exponentially large dimension and Betti number are necessary, but insufficient conditions, for superpolynomial advantage. We then introduce and analyze specific problem examples which have parameters in the regime where superpolynomial advantages may be achieved, and argue that quantum circuits with tens of billions of Toffoli gates can solve seemingly classically intractable instances. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Bifurcation Buckling Analysis and Non-Linear Collapse Analysis of Teardrop Shaped Vacuum Chamber

The Spallation Neutron Source (SNS) accelerator is being upgraded to increase the beam power from 1.4MW at 1GeV to 2.8MW at 1.3GeV. The currents in the middle two injection chicane magnets cannot simply be scaled up to accommodate the increased injection energy of 1.3GeV due to potential excessive H- stripping; the magnets must be replaced with longer, lower-field magnets and the associated vacuum chambers need to be redesigned. A new teardrop-shaped vacuum chamber was initially designed to accommodate the new magnets and the updated beam paths and instrumentation. This paper focuses on the structural stability study of the teardrop shape vacuum chamber based on buckling analysis. Protection against collapse from buckling according to the ASME BPVC requirement has been evaluated in depth. First, a Type-1 bifurcation buckling analysis using a linear eigenvalue solution to determine the critical load factor was performed. Subsequently, a Type-3 nonlinear collapse analysis was conducted using the static Riks method with elastic-plastic material properties and imperfections explicitly considered in the model geometry. The critical buckling load for the teardrop shape vacuum chamber was confidently estimated based upon this two-stage approach.

Jiang, Hao↗

DOE OSTI2018

Development of a Library for Conducting Monte Carlo Tallies on Heterogeneous Systems

A library is introduced that enables users to conduct Monte Carlo tallies on heterogeneous computing systems. The library can be built with or linked to a Monte Carlo transport code to provide tally capabilities for the project. The library provides a set of tools and an interface for constructing tallies that can be computed on CPUs or GPUs regardless of where the sample data was generated. The library can be incorporated into existing Monte Carlo transport codes at both the research and production level with minimal intrusion into the transport code. The tally library is capable of computing a variety of tallies including track-length histogram (mesh) tallies, collisionbased kernel density estimators, functional expansion tallies, eigenvalue sensitivity coefficients via iterated fission probability, and sensitivities of reaction rates or adjoint-weighted quantities via differential operator sampling. The parallelization methods are discussed and speedups are shown for 2-D and 3-D problems with comparisons to both the tally library CPU implementations as well as the tally capabilities in the host transport code. Performance results and examples are shown for MCNP, MCATK, and OpenMC.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Development of a Representative Molten Chloride Fast Reactor Model to Assess the Impact of Nuclear Data

The SCALE code system was employed to conduct a preliminary investigation of nuclear data impacts for a fast spectrum molten chloride salt reactor. A computationally effective depletion model that is representative of the reactor system was successfully developed and used to conduct fuel depletion simulations. Development of this model draws from the SLICE method that was developed at Oak Ridge National Laboratory to enable generation of fuel compositions for an advanced reactor core at equilibrium operation. Eigenvalue uncertainty calculations using the ENDF/B-VII.1 nuclear data library were performed for the reactor in the fresh fuel state and an irradiated fuel state. It was determined that the primary driver of eigenvalue uncertainty was the uncertainty in the 235U (n, 𝛾) cross section. Uncertainty calculation results from this study were compared to results available for a different fast system, a sodium-cooled fast reactor, to confirm similarities and identify differences with respect to nuclear data impacts between the two fast advanced reactor systems.

Hirji, Rakim [Georgia Institute of Technology]↗

DOE OSTI2022

Demonstration of MOOSE-based Griffin reactor physics, code for heterogeneous lead-cooled fast reactor analysis

The MOOSE-based reactor physics code Griffin was assessed on a heterogeneous pin-resolved model of a prototype lead-cooled fast reactor assembly. This model was developed in preparation for future use in MOOSE-based multiphysics calculations for computing hot channel factors. Heterogeneous multigroup cross sections were prepared using the fast reactor multi-group cross section processing code MC{sup 2}-3 using a two-step method. Griffin simulations were performed using the DFEM-SN solver on 576 cores on Argonne's LCRC cluster. Diffusion-based acceleration methods were applied (NDA and CMFD). Reference solutions were generated with continuous energy MCNP and the hybrid MOC/finite element solver PROTEUS-MOC for code-to-code comparison. Space-angle convergence studies were conducted to observe convergence in k-eigenvalue and axial pin power distributions. The fully resolved Griffin calculation was within 68 pcm of the MCNP eigenvalue and exhibited max 1.2% relative error in the axial pin power distribution. Griffin produced nearly identical results to PROTEUS-MOC when using the same 9-group multigroup cross-section set. Griffin demonstrated favorable scaling in wall-clock time and memory usage when using diffusion-based acceleration methods. Griffin is capable of simulating the pin-resolved heterogeneous LFR assembly with good accuracy and performance, and is suitable for future use in coupled high-fidelity hot channel factor simulations. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

$O(N)$ ab initio calculation scheme for large-scale moiré structures

Here we present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for the ground state is performed with the O(N) Krylov subspace method implemented in openmx. Second, the crystal momentum-dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of the Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures down to the first magic angle (θ = 1.08°) with high enough accuracy at affordable costs. The band structures are in good agreement with those from tight-binding models, continuum models, plane-wave pseudopotential based ab initio calculations, and experimental observations. This method is also shown to be efficient in twisted double-bilayer graphene and bilayer WSe 2 . We think this two-step method can play a crucial role in other twisted two-dimensional materials, especially those with much more complex band structure and where the effective model is hard to construct.

36 MATERIALS SCIENCE↗