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DOE OSTI2012

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decomposition corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

stacked predictive sparse decomposition (SPSD) v1.0

It is an unsupervised representation algorithm used to learn morphometric properties from cellular objects. Many similar/identical open source implementations are widely available in tensorflow, pytorch, etc. And ours is implemented in matlab.

Chang, Hang↗

DOE OSTI2023

Relativistic resolution-of-the-identity with Cholesky integral decomposition

In this study, we present an efficient integral decomposition approach called the restricted-kinetic-balance resolution-of-the-identity (RKB-RI) algorithm, which utilizes a tunable RI method based on the Cholesky integral decomposition for in-core relativistic quantum chemistry calculations. The RKB-RI algorithm incorporates the restricted-kinetic-balance condition and offers a versatile framework for accurate computations. Notably, the Cholesky integral decomposition is employed not only to approximate symmetric large-component electron repulsion integrals but also those involving small-component basis functions. In addition to comprehensive error analysis, we investigate crucial conditions, such as the kinetic balance condition and variational stability, which underlie the applicability of Dirac relativistic electronic structure theory. Here we compare the computational cost of the RKB-RI approach with the full in-core method to assess its efficiency. To evaluate the accuracy and reliability of the RKB-RI method proposed in this work, we employ actinyl oxides as benchmark systems, leveraging their properties for validation purposes. This investigation provides valuable insights into the capabilities and performance of the RKB-RI algorithm and establishes its potential as a powerful tool in the field of relativistic quantum chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

The effect of load imbalances on the performance of Monte Carlo algorithms in LWR analysis

A model is developed to predict the impact of particle load imbalances on the performance of domain-decomposed Monte Carlo neutron transport algorithms. Expressions for upper bound performance “penalties” are derived in terms of simple machine characteristics, material characterizations and initial particle distributions. The hope is that these relations can be used to evaluate tradeoffs among different memory decomposition strategies in next generation Monte Carlo codes, and perhaps as a metric for triggering particle redistribution in production codes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Scalable FBP decomposition for cone-beam CT reconstruction

Filtered Back-Projection (FBP) is a fundamental compute intense algorithm used in tomographic image reconstruction. Cone-Beam Computed Tomography (CBCT) devices use a cone-shaped X-ray beam, in comparison to the parallel beam used in older CT generations. Distributed image reconstruction of cone-beam datasets typically relies on dividing batches of images into different nodes. This simple input decomposition, however, introduces limits on input/output sizes and scalability.We propose a novel decomposition scheme and reconstruction algorithm for distributed FPB. This scheme enables arbitrarily large input/output sizes, eliminates the redundancy arising in the end-to-end pipeline and improves the scalability by replacing two communication collectives with only one segmented reduction. Finally, we implement the proposed decomposition scheme in a framework that is useful for all current-generation CT devices (7th gen). In our experiments using up to 1024 GPUs, our framework can construct 40963 volumes, for real-world datasets, in under 16 seconds (including I/O).

Chen, Peng↗

DOE OSTI2014

Properties OF M31. V. 298 eclipsing binaries from PAndromeda

The goal of this work is to conduct a photometric study of eclipsing binaries in M31. We apply a modified box-fitting algorithm to search for eclipsing binary candidates and determine their period. We classify these candidates into detached, semi-detached, and contact systems using the Fourier decomposition method. We cross-match the position of our detached candidates with the photometry from Local Group Survey and select 13 candidates brighter than 20.5 mag in V. The relative physical parameters of these detached candidates are further characterized with the Detached Eclipsing Binary Light curve fitter (DEBiL) by Devor. We will follow up the detached eclipsing binaries spectroscopically and determine the distance to M31.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Quantum Fourier transform revisited

Summary The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the quantum Fourier transform (QFT) can be derived by further decomposing the diagonal factors of the FFT matrix decomposition into products of matrices with Kronecker product structure. We analyze the implication of this Kronecker product structure on the discrete Fourier transform of rank‐1 tensors on a classical computer. We also explain why such a structure can take advantage of an important quantum computer feature that enables the QFT algorithm to attain an exponential speedup on a quantum computer over the FFT algorithm on a classical computer. Further, the connection between the matrix decomposition of the DFT matrix and a quantum circuit is made. We also discuss a natural extension of a radix‐2 QFT decomposition to a radix‐ d QFT decomposition. No prior knowledge of quantum computing is required to understand what is presented in this paper. Yet, we believe this paper may help readers to gain some rudimentary understanding of the nature of quantum computing from a matrix computation point of view.

Camps, Daan↗

DOE OSTI2017

Quantified Gamow shell model interaction for p s d -shell nuclei

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5 ≤ A ≲ 12 at the p-sd-shell interface. Method: The one-body potential of the 4 He core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ 2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon- 4 He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A = 9 . A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. In conclusion: The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the psd region of the nuclear chart.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Simulations of relativistic quantum plasmas using real-time lattice scalar QED

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may also be computed using quantum parallelism in the future.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

From Escherichia coli mutant 13 C labeling data to a core kinetic model: A kinetic model parameterization pipeline

Kinetic models of metabolic networks offer the promise of quantitative phenotype prediction. The mechanistic characterization of enzyme catalyzed reactions allows for tracing the effect of perturbations in metabolite concentrations and reaction fluxes in response to genetic and environmental perturbation that are beyond the scope of stoichiometric models. In this study, we develop a two-step computational pipeline for the rapid parameterization of kinetic models of metabolic networks using a curated metabolic model and available 13 C-labeling distributions under multiple genetic and environmental perturbations. The first step involves the elucidation of all intracellular fluxes in a core model of E. coli containing 74 reactions and 61 metabolites using 13 C-Metabolic Flux Analysis ( 13 C-MFA). Here, fluxes corresponding to the mid-exponential growth phase are elucidated for seven single gene deletion mutants from upper glycolysis, pentose phosphate pathway and the Entner-Doudoroff pathway. The computed flux ranges are then used to parameterize the same (i.e., k-ecoli74) core kinetic model for E. coli with 55 substrate-level regulations using the newly developed K-FIT parameterization algorithm. The K-FIT algorithm employs a combination of equation decomposition and iterative solution techniques to evaluate steady-state fluxes in response to genetic perturbations. k-ecoli74 predicted 86% of flux values for strains used during fitting within a single standard deviation of 13 C-MFA estimated values. By performing both tasks using the same network, errors associated with lack of congruity between the two networks are avoided, allowing for seamless integration of data with model building. Product yield predictions and comparison with previously developed kinetic models indicate shifts in flux ranges and the presence or absence of mutant strains delivering flux towards pathways of interest from training data significantly impact predictive capabilities. Using this workflow, the impact of completeness of fluxomic datasets and the importance of specific genetic perturbations on uncertainties in kinetic parameter estimation are evaluated.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Development of Thermal Tomography Imaging System for In-Service Nondestructive Evaluation of Additively Manufactured Components

36 MATERIALS SCIENCE↗

DOE OSTI2020

Pulsed Thermal Tomography Nondestructive Examination of Additively Manufactured Reactor Materials (Second Annual Progress Report)

Additive manufacturing (AM) is an emerging method for cost-efficient fabrication of nuclear reactor parts. AM of metallic structures for nuclear energy applications is currently based on laser powder bed fusion (LPBF) process, which can introduce internal material flaws, such as pores and anisotropy. Integrity of AM structures needs to be evaluated nondestructively because material flaws could lead to premature failures due to exposure to high temperature, radiation and corrosive environment in a nuclear reactor. Thermal tomography (TT) provides a capability for non-destructive evaluation of sub-surface defects in arbitrary size structures. Thermal tomography is a computational method for heat diffusion-based imaging of solids, which provides 3D visualization of data from flash thermography measurements. We investigate thermal tomography imaging and nondestructive evaluation of stainless steel and nickel super alloy metallic structures produced with laser powder bed fusion (LPBF) additive manufacturing (AM) process. Metallic structures produced with LPBF contain defects, and there are limited capabilities to evaluate these structures non-destructively. Thermal tomography reconstruction of 3D apparent spatial effusivity provides information about AM structure geometry and internal material flaws. We study performance of thermal tomography in imaging of metallic structures through COMSOL computer simulations of transient heat transfer, and through reconstruction of data obtained from experimental measurements. Reconstruction of internal defects is investigated using a stainless steel 316L specimen with flat bottom hole (FBH) indentations, and Inconel 718 plate produced with laser powder bed fusion (LPBF) method, which contains imprinted hemispherical shape low density regions containing non-sintered metallic powder. The FBH’s have the same sizes as the imprinted defects in the LPBF specimens, but offer better imaging contrast. Thermal tomography reconstructions provide visualizations of internal defects, and allow for estimation of their sizes and locations. Detection sensitivity of TT is limited by noises. We investigate separation of signal from noise in thermography images using several machine learning (ML) methods, including new spatio-temporal blind source separation (STBSS) and spatio-temporal sparse dictionary learning (STSDL) methods. Performance of the ML methods is benchmarked using thermography data obtained from imaging stainless steel 316L and Inconel 718 specimens produced LPBF method with imprinted calibrated porosity defects. The ML methods are ranked by F-score and execution runtime. Finally, we investigate TT of AM stainless steel 316L specimen with imprinted internal porosity defects using relatively low-cost, small form factor infrared (IR) camera based on uncooled micro bolometer detector. Sparse coding related K-means singular value decomposition (SVD) machine learning, image processing algorithms are developed to improve quality of TT images through removal of Additive white Gaussian noise without blurring the images. Following initial qualification of an AM component for deployment in a nuclear reactor, a compact TT can also be used for in-service nondestructive evaluation (NDE). With capability to perform in-service NDE of the AM component lifecycle, TT data can be used for development of a component digital twin.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Time dependent supervisory control update with FARM using rolling window

This report describes improvements to the Feasible Actuator Range Modifier (FARM) component of the RAVEN-based HYBRID framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON plug-in that solves the power dispatch problem. The solution to the dispatch problem involves economically optimal dispatches that satisfy limits on production variables and their rates of variation (explicit constraints) as well as process variables tied to the service life of equipment (implicit constraints). FARM serves to validate or confirm that a HERON solution for explicit constraints also satisfies the implicit constraints. FARM-alpha was released by Argonne National Laboratory in January 2021 followed by FARM-Beta in January 2022 with the latter providing increased flexibility for the user. In this report, FARM-Gamma, the latest version of the code, is described. The major improvement is the implementation of a system identification algorithm based on the Dynamic Mode Decomposition with Control (DMDc) coupled with a “Rolling Window” scheme that allows obtaining linear time-varying state-space models. This feature equips FARM with the most accurate approximation of system dynamics, and it relieves the user from the burden of performing an exhaustive off-line characterization of the dynamics. FARM-Gamma capabilities are assessed by solving the power dispatch problem for a representative IES unit. The simulation times corresponding to the different releases are estimated and compared. These values capture the increasing computational burden of the successively higher fidelity state-space models adopted by FARM-Alpha, FARM-Beta and FARM-Gamma. The code implementation provides significant flexibility, i.e., the user can always select the most suitable version of FARM according to the problem to be solved and the available computational resources. It is anticipated that FARM will play a role in addressing several future IES applications. We outline how it can support the coordinated management and safe operation of a nuclear plant coupled to industrial processes to produce hydrogen and synfuels.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

A weighted state redistribution algorithm for embedded boundary grids

State redistribution is an algorithm that stabilizes cut cells for embedded boundary grid methods. This work extends the earlier algorithm in several important ways. First, state redistribution is extended to three spatial dimensions. Second, we discuss several algorithmic changes and improvements motivated by the more complicated cut cell geometries that can occur in higher dimensions. In particular, we introduce a weighted version with less dissipation in an easily generalizable framework. Third, we demonstrate that state redistribution can also stabilize a solution update that includes both advective and diffusive contributions. Notably, the stabilization algorithm is shown to be effective for incompressible as well as compressible reacting flows. Finally, we discuss the implementation of the algorithm for several exascale-ready simulation codes based on AMReX, demonstrating ease of use in combination with domain decomposition, hybrid parallelism and complex physics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Iterative image-domain decomposition for dual-energy CT

Purpose: Dual energy CT (DECT) imaging plays an important role in advanced imaging applications due to its capability of material decomposition. Direct decomposition via matrix inversion suffers from significant degradation of image signal-to-noise ratios, which reduces clinical values of DECT. Existing denoising algorithms achieve suboptimal performance since they suppress image noise either before or after the decomposition and do not fully explore the noise statistical properties of the decomposition process. In this work, the authors propose an iterative image-domain decomposition method for noise suppression in DECT, using the full variance-covariance matrix of the decomposed images. Methods: The proposed algorithm is formulated in the form of least-square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, the authors include the inverse of the estimated variance-covariance matrix of the decomposed images as the penalty weight in the least-square term. The regularization term enforces the image smoothness by calculating the square sum of neighboring pixel value differences. To retain the boundary sharpness of the decomposed images, the authors detect the edges in the CT images before decomposition. These edge pixels have small weights in the calculation of the regularization term. Distinct from the existing denoising algorithms applied on the images before or after decomposition, the method has an iterative process for noise suppression, with decomposition performed in each iteration. The authors implement the proposed algorithm using a standard conjugate gradient algorithm. The method performance is evaluated using an evaluation phantom (Catphan©600) and an anthropomorphic head phantom. The results are compared with those generated using direct matrix inversion with no noise suppression, a denoising method applied on the decomposed images, and an existing algorithm with similar formulation as the proposed method but with an edge-preserving regularization term. Results: On the Catphan phantom, the method maintains the same spatial resolution on the decomposed images as that of the CT images before decomposition (8 pairs/cm) while significantly reducing their noise standard deviation. Compared to that obtained by the direct matrix inversion, the noise standard deviation in the images decomposed by the proposed algorithm is reduced by over 98%. Without considering the noise correlation properties in the formulation, the denoising scheme degrades the spatial resolution to 6 pairs/cm for the same level of noise suppression. Compared to the edge-preserving algorithm, the method achieves better low-contrast detectability. A quantitative study is performed on the contrast-rod slice of Catphan phantom. The proposed method achieves lower electron density measurement error as compared to that by the direct matrix inversion, and significantly reduces the error variation by over 97%. On the head phantom, the method reduces the noise standard deviation of decomposed images by over 97% without blurring the sinus structures. Conclusions: The authors propose an iterative image-domain decomposition method for DECT. The method combines noise suppression and material decomposition into an iterative process and achieves both goals simultaneously. By exploring the full variance-covariance properties of the decomposed images and utilizing the edge predetection, the proposed algorithm shows superior performance on noise suppression with high image spatial resolution and low-contrast detectability.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2017

Reactivity of alkyl iodides in molecular decomposition reactions

The experimental results for the concerted molecular decomposition of alkyl iodides RI to olefin and HI were analyzed in terms of the intersecting parabolas model (IPM). The activation energies (E) and rate constants (k) of the earlier unstudied reactions of the concerted molecular decomposition of RI were calculated on the basis of the enthalpy of the reaction and IPM algorithms. The factors that influence on E of RI decay were established: the enthalpy of the reaction, the energy of stabilization of radical R*, the length and force constant of the C—I bond, and the size of the halogen atom. The values of E and k for the backward reactions of HI addition to olefins were estimated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2012

Robust volume calculations for Constructive Solid Geometry (CSG) components in Monte Carlo transport calculations

In this paper we consider a new generalized algorithm for the efficient calculation of component object volumes given their equivalent constructive solid geometry (CSG) definition. The new method relies on domain decomposition to recursively subdivide the original component into smaller pieces with volumes that can be computed analytically or stochastically, if needed. Unlike simpler brute-force approaches, the proposed decomposition scheme is guaranteed to be robust and accurate to within a user-defined tolerance. The new algorithm is also fully general and can handle any valid CSG component definition, without the need for additional input from the user. The new technique has been specifically optimized to calculate volumes of component definitions commonly found in models used for Monte Carlo particle transport simulations for criticality safety and reactor analysis applications. However, the algorithm can be easily extended to any application which uses CSG representations for component objects. The paper provides a complete description of the novel volume calculation algorithm, along with a discussion of the conjectured error bounds on volumes calculated within the method. In addition, numerical results comparing the new algorithm with a standard stochastic volume calculation algorithm are presented for a series of problems spanning a range of representative component sizes and complexities. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗