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DOE OSTI2018

Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind

In this paper, Legendre spectral projection methods are applied for the Volterra integral equations of second kind with a smooth kernel. We prove that the approximate solutions of the Legendre Galerkin and Legendre collocation methods converge to the exact solution with the order O(n{sup −r}) in L{sup 2}-norm and order O(n{sup −r+(1/2)}) in infinity norm, and the iterated Legendre Galerkin solution converges with the order O(n{sup −2r}) in both L{sup 2}-norm and infinity norm, whereas the iterated Legendre collocation solution converges with the order O(n{sup −r}) in both L{sup 2}-norm and infinity norm, n being the highest degree of Legendre polynomials employed in the approximation and r being the smoothness of the kernels. We have also considered multi-Galerkin method and its iterated version, and prove that the iterated multi-Galerkin solution converges with the order O(n{sup −3r}) in both infinity and L{sup 2} norm. Numerical examples are given to illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Tensorized Feature Spaces for Feature Explosion

In this paper 1 1 This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-000R22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan) This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-000R22725., we present a novel framework that uses tensor factorization to generate richer feature spaces for pixel classification in hyperspectral images. In particular, we assess the performance of different tensor rank decomposition methods as compared to the traditional kernel-based approaches for the hyperspectral image classification problem. We propose Orion, which takes as input a hyperspectral image tensor and a rank and outputs an enhanced feature space from the factor matrices of the decomposed tensor. Our method is a feature explosion technique that inherently maps low dimensional input space in $\mathbb{R}^{K}$ to high dimensional space in $\mathbb{R}^{R}$ , where $R\gg K$ , say in the order of 1000x, like a kernel. We show how the proposed method exploits the multi-linear structure of hyperspectral three dimensional tensor. We demonstrate the effectiveness of our method with experiments on three publicly available hyperspectral datasets with labeled pixels and compare their classification performance against traditional linear and non-linear supervised learning methods such as SVM with Linear, Polynomial, RBF kernels, and the Multi-Layer Perceptron model. Finally, we explore the relationship between the rank of the tensor decomposition and the classification accuracy using several hyperspectral datasets with ground truth.

Pasricha, Ravdeep Singh↗

DOE OSTI2018

Partially coherent ptychography by gradient decomposition of the probe

Coherent ptychographic imaging experiments often discard the majority of the flux from a light source to define the coherence of the illumination. Even when the coherent flux is sufficient, the stability required during an exposure is another important limiting factor. Partial coherence analysis can considerably reduce these limitations. A partially coherent illumination can often be written as the superposition of a single coherent illumination convolved with a separable translational kernel. This article proposes the gradient decomposition of the probe (GDP), a model that exploits translational kernel separability, coupling the variances of the kernel with the transverse coherence. An efficient first-order splitting algorithm ( GDP-ADMM ) for solving the proposed nonlinear optimization problem is described. Numerical experiments demonstrate the effectiveness of the proposed method with Gaussian and binary kernel functions in fly-scan measurements. Remarkably, GDP-ADMM using nanoprobes produces satisfactory results even when the ratio between the kernel width and the beam size is more than one, or when the distance between successive acquisitions is twice as large as the beam width.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

WE-EF-BRA-07: High Performance Preclinical Irradiation Through Optimized Dual Focal Spot Dose Painting and Online Virtual Isocenter Radiation Field Targeting

Purpose: Advances in radiotherapy practice facilitated by collimation systems to shape radiation fields and image guidance to target these conformal beams have motivated proposals for more complex dose patterns to improve the therapeutic ratio. Recent progress in small animal radiotherapy platforms has provided the foundation to validate the efficacy of such interventions, but robustly delivering heterogeneous dose distributions at the scale and accuracy demanded by preclinical studies remains challenging. This work proposes a dual focal spot optimization method to paint spatially heterogeneous dose regions and an online virtual isocenter targeting method to accurately target the dose distributions. Methods: Two-dimensional dose kernels were empirically measured for the 1 mm diameter circular collimator with radiochromic film in a solid water phantom for the small and large x-ray focal spots on the X-RAD 225Cx microirradiator. These kernels were used in an optimization framework which determined a set of animal stage positions, beam-on times, and focal spot settings to optimally deliver a given desired dose distribution. An online method was developed which defined a virtual treatment isocenter based on a single image projection of the collimated radiation field. The method was demonstrated by optimization of a 6 mm circular 2 Gy target adjoining a 4 mm semicircular avoidance region. Results: The dual focal spot technique improved the optimized dose distribution with the proportion of avoidance region receiving more than 0.5 Gy reduced by 40% compared to the large focal spot technique. Targeting tests performed by irradiating ball bearing targets on radiochromic film pieced revealed the online targeting method improved the three-dimensional accuracy from 0.48 mm to 0.15 mm. Conclusion: The dual focal spot optimization and online virtual isocenter targeting framework is a robust option for delivering dose at the preclinical level and provides a new experimental option for unique radiobiological investigations This work is supported, in part, by the Natural Sciences and Engineering Research Council of Canada and a Mitacs-Accelerate fellowship. P.E. Lindsay, and D.A. Jaffray are listed as inventors of the system described herein. This system has been licensed to Precision X-Ray Inc. for commercial development.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2010

A Scalable Parallel Algorithm for Large-Scale Protein Sequence Homology Detection

Protein sequence homology detection is a fundamental problem in computational molecular biology, with a pervasive application in nearly all analyses that aim to structurally and functionally characterize protein molecules. While detecting homology between two protein sequences is computationally inexpensive, detecting pairwise homology at a large-scale becomes prohibitive, requiring millions of CPU hours. Yet, there is currently no efficient method available to parallelize this kernel. In this paper, we present the key characteristics that make this problem particularly hard to parallelize, and then propose a new parallel algorithm that is suited for large-scale protein sequence data. Our method, called pGraph, is designed using a hierarchical multiple-master multiple-worker model, where the processor space is partitioned into subgroups and the hierarchy helps in ensuring the workload is load balanced fashion despite the inherent irregularity that may originate in the input. Experimental evaluation demonstrates that our method scales linearly on all input sizes tested (up to 640K sequences) on a 1,024 node supercomputer. In addition to demonstrating strong scaling, we present an extensive study of the various components of the system and related parametric studies.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2014

WE-E-BRE-04: Dual Focal Spot Dose Painting for Precision Preclinical Radiobiological Investigations

Purpose: Recent progress in small animal radiotherapy systems has provided the foundation for delivering the heterogeneous, millimeter scale dose distributions demanded by preclinical radiobiology investigations. Despite advances in preclinical dose planning, delivery of highly heterogeneous dose distributions is constrained by the fixed collimation systems and large x-ray focal spot common in small animal radiotherapy systems. This work proposes a dual focal spot dose optimization and delivery method with a large x-ray focal spot used to deliver homogeneous dose regions and a small focal spot to paint spatially heterogeneous dose regions. Methods: Two-dimensional dose kernels were measured for a 1 mm circular collimator with radiochromic film at 10 mm depth in a solid water phantom for the small and large x-ray focal spots on a recently developed small animal microirradiator. These kernels were used in an optimization framework which segmented a desired dose distribution into low- and high-spatial frequency regions for delivery by the large and small focal spot, respectively. For each region, the method determined an optimal set of stage positions and beam-on times. The method was demonstrated by optimizing a bullseye pattern consisting of 0.75 mm radius circular target and 0.5 and 1.0 mm wide rings alternating between 0 and 2 Gy. Results: Compared to a large focal spot technique, the dual focal spot technique improved the optimized dose distribution: 69.2% of the optimized dose was within 0.5 Gy of the intended dose for the large focal spot, compared to 80.6% for the dual focal spot method. The dual focal spot design required 14.0 minutes of optimization, and will require 178.3 minutes for automated delivery. Conclusion: The dual focal spot optimization and delivery framework is a novel option for delivering conformal and heterogeneous dose distributions at the preclinical level and provides a new experimental option for unique radiobiological investigations. Funding Support: this work is supported by funding the National Sciences and Engineering Research Council of Canada, and a Mitacs-accelerate fellowship. Conflict of Interest: Dr. Lindsay and Dr. Jaffray are listed as inventors of the small animal microirradiator described herein. This system has been licensed for commercial development.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

A high-order computational framework for particle-resolved simulations of disperse multiphase flows

This work presents a high-order numerical approach for particle-resolved simulations of disperse multiphase flows, where the Navier-Stokes equations for fluid flow are solved using a high-order spectral element method in the Eulerian framework, and the particle phase is directly simulated with a discrete element method. The coupling between particles and fluids is explicitly handled using an adapted direct-forcing immersed boundary method. Unlike the conventional schemes, a high-order barycentric Lagrange interpolation method and a Gaussian projection kernel are used to ensure accurate momentum exchange between local boundary points and surrounding fluid nodes in the framework of high-order fluid solver. Benchmark tests of increasing complexity are conducted to demonstrate the accuracy and efficiency of our method. Here, it is found that our approach exhibits an excellent convergence performance, as the fluid element/grid is refined and the number of boundary points increases. Compared to conventional low-order methods, the proposed high-order framework enables the use of substantially larger fluid elements while maintaining high accuracy in modeling fluid-particle interactions, owing to the enhanced resolution of high-order basis functions. Moreover, since the primary unknowns are stored at element or grid nodes, the high-order approach offers improved efficiency in both CPU memory usage and total computational cost.

42 ENGINEERING↗

DOE OSTI2023

Simulation of Mechanical Fractionation of Chopped Whole-Plant Corn (WPC) Using Discrete Element Method (DEM)

Fractionating whole-plant corn (WPC) in a single-pass harvesting system requires studies on the WPC-to-equipment interaction for improved property control, as well as mechanical and air-driven separation processes compared to the traditional multi-pass grain and stover harvesting system. The discrete element method (DEM) technique has the potential to simulate WPC mechanical fractionation and support simulation-based design of WPC separation processes. In this study, methods to develop DEM particle models of WPC (kernel, cob, stalk, and husk) and their material properties for simulating mass fractionation using the ASABE standard mechanical shaker were proposed. Measurement was done on the axial dimensions (major, intermediate, and minor) and mass of each WPC type (mean sample size is 56), sampled from single-pass harvesting. Applying gaussian multivariate regression and bootstrapping re-sampling techniques, a DEM particle approximate to each WPC was developed. Sensitivity analysis of the DEM Young‘s modulus, Poisson‘s ratio, and interaction parameters of coefficient of restitution, coefficient of rolling friction, and coefficient of static friction on mass fraction was performed after 156 ASABE sieve-shaking DEM simulation runs, generated using Latin Hypercube Design (LHD) design of experiment (DOE) from 19 DEM material parameters. DEM simulation using Hertz-Mindlin with flexible bond contact laws and DOE optimized material properties successfully reproduced the mass fractions retained in ASABE sieves at 9.8% mean relative error and a coefficient of determination of R2 = 0.87. Here, the DEM methodology developed for mechanical WPC mass fractionation could be deployed to perform virtual design of feedstock handling equipment and performance analysis of mechanical fraction systems.

09 BIOMASS FUELS↗

DOE OSTI2019

Scalable Causal Graph Learning through a Deep Neural Network

Learning the causal graph in a complex system is crucial for knowledge discovery and decision making, yet it remains a challenging problem because of the unknown nonlinear interaction among system components. Most of the existing methods either rely on predefined kernel or data distribution, or they focus simply on the causality between a single target and the remaining system. This work presents a deep neural network for scalable causal graph learning (SCGL) through low-rank approximation. The SCGL model can explore nonlinearity on both temporal and intervariable relationships without any predefined kernel or distribution assumptions. Through low-rank approximation, the noise influence is reduced, and better accuracy and high scalability are achieved. Experiments using synthetic and real-world datasets show that our SCGL algorithm outperforms existing state-of-the-art methods for causal graph learning.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2010

MCNP Super Lattice Method for VHTR ORIGEN2.2 Nuclear Library Improvement Based on ENDF/B-VII

The advanced Very High Temperature gas-cooled Reactor (VHTR) achieves simplification of safety through reliance on innovative features and passive systems. One of the VHTRs innovative features is the reliance on ceramic-coated fuel particles to retain the fission products under extreme accident conditions. The effect of the random fuel kernel distribution in the fuel prismatic block creates a double-heterogeneous lattice, which needs to be addressed through the use of the newly developed prismatic super Kernel-by-Kernel Fuel (KbKF) lattice model method. Based on the new ENDF/B-VII nuclear cross section evaluated data, the developed KbKF super lattice model was then used with MCNP to calculate the material isotopes neutron reaction rates, such as, (n,?); (n,n’); (n,2n’); (n,f); (n,p); (n,?). Then, the MCNP-calculated results are rearranged to generate a set of new libraries “VHTRXS.lib,” for the ORIGEN2.2 isotopes depletion and build-up analysis code. The libraries contain one group cross section data for the structural light elements, actinides, and fission products that can be applied in the VHTR related fuel burnup and material transmutation analysis codes. The efficiency and ease of use of the MCNP method to generate and update the ORIGEN2.2 one-group spectrum weighed cross section library for VHTR was demonstrated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

Robust Online Monitoring for Calibration Assessment of Transmitters and Instrumentation

Robust online monitoring (OLM) technologies are expected to enable the extension or elimination of periodic sensor calibration intervals in operating and new reactors. These advances in OLM technologies will improve the safety and reliability of current and planned nuclear power systems through improved accuracy and increased reliability of sensors used to monitor key parameters. In this article, we discuss an overview of research being performed within the Nuclear Energy Enabling Technologies (NEET)/Advanced Sensors and Instrumentation (ASI) program, for the development of OLM algorithms to use sensor outputs and, in combination with other available information, 1) determine whether one or more sensors are out of calibration or failing and 2) replace a failing sensor with reliable, accurate sensor outputs. Algorithm development is focused on the following OLM functions: • Signal validation • Virtual sensing • Sensor response-time assessment These algorithms incorporate, at their base, a Gaussian Process-based uncertainty quantification (UQ) method. Various plant models (using kernel regression, GP, or hierarchical models) may be used to predict sensor responses under various plant conditions. These predicted responses can then be applied in fault detection (sensor output and response time) and in computing the correct value (virtual sensing) of a failing physical sensor. The methods being evaluated in this work can compute confidence levels along with the predicted sensor responses, and as a result, may have the potential for compensating for sensor drift in real-time (online recalibration). Evaluation was conducted using data from multiple sources (laboratory flow loops and plant data). Ongoing research in this project is focused on further evaluation of the algorithms, optimization for accuracy and computational efficiency, and integration into a suite of tools for robust OLM that are applicable to monitoring sensor calibration state in nuclear power plants.

fault detection↗

DOE OSTI2011

Three-dimensional photodissociation in strong laser fields: Memory-kernel effective-mode expansion

We introduce a method for the efficient computation of non-Markovian quantum dynamics for strong (and time-dependent) system-bath interactions. The past history of the system dynamics is incorporated by expanding the memory kernel in exponential functions thereby transforming in an exact fashion the non-Markovian integrodifferential equations into a (larger) set of ''effective modes'' differential equations (EMDE). We have devised a method which easily diagonalizes the EMDE, thereby allowing for the efficient construction of an adiabatic basis and the fast propagation of the EMDE in time. We have applied this method to three-dimensional photodissociation of the H{sub 2}{sup +} molecule by strong laser fields. Our calculations properly include resonance-Raman scattering via the continuum, resulting in extensive rotational and vibrational excitations. The calculated final kinetic and angular distribution of the photofragments are in overall excellent agreement with experiments, both when transform-limited pulses and when chirped pulses are used.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Generalized quantum master equations in and out of equilibrium: When can one win?

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Master Formula for One-Loop Renormalization of Bosonic SMEFT Operators

Using background-field method and super-heat-kernel expansion, we derive a master formula for the one-loop UV divergences of the bosonic dimension-6 operators in Standard Model Effective Field Theory (SMEFT). This approach reduces the calculation of all the UV divergences to algebraic manipulations. Using this formula we corroborate results in the literature for the one-loop anomalous dimension matrix of SMEFT obtained via diagrammatic methods, considering contributions from the operators $X^3, \phi^6, \phi^4 D^2, X^2 \phi^2$ of the Warsaw basis. The formula is derived in a general way and can be applied to other quantum field theories as well.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Acceleration of tensor-product operations for high-order finite element methods

This article is devoted to graphics processing unit (GPU) kernel optimization and performance analysis of three tensor-product operations arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving close to peak performance for these operators requires extensive optimization because of the operators’ properties: low arithmetic intensity, tiered structure, and the need to store intermediate results during the kernel execution. We give a guided overview of optimization strategies and we present a performance model that allows us to compare the efficacy of these optimizations against an empirically calibrated roofline.

Świrydowicz, Kasia↗

DOE OSTI2015

SU-E-T-423: Fast Photon Convolution Calculation with a 3D-Ideal Kernel On the GPU

Purpose: The calculation time is a trade-off for improving the accuracy of convolution dose calculation with fine calculation spacing of the KERMA kernel. We investigated to accelerate the convolution calculation using an ideal kernel on the Graphic Processing Units (GPU). Methods: The calculation was performed on the AMD graphics hardware of Dual FirePro D700 and our algorithm was implemented using the Aparapi that convert Java bytecode to OpenCL. The process of dose calculation was separated with the TERMA and KERMA steps. The dose deposited at the coordinate (x, y, z) was determined in the process. In the dose calculation running on the central processing unit (CPU) of Intel Xeon E5, the calculation loops were performed for all calculation points. On the GPU computation, all of the calculation processes for the points were sent to the GPU and the multi-thread computation was done. In this study, the dose calculation was performed in a water equivalent homogeneous phantom with 150{sup 3} voxels (2 mm calculation grid) and the calculation speed on the GPU to that on the CPU and the accuracy of PDD were compared. Results: The calculation time for the GPU and the CPU were 3.3 sec and 4.4 hour, respectively. The calculation speed for the GPU was 4800 times faster than that for the CPU. The PDD curve for the GPU was perfectly matched to that for the CPU. Conclusion: The convolution calculation with the ideal kernel on the GPU was clinically acceptable for time and may be more accurate in an inhomogeneous region. Intensity modulated arc therapy needs dose calculations for different gantry angles at many control points. Thus, it would be more practical that the kernel uses a coarse spacing technique if the calculation is faster while keeping the similar accuracy to a current treatment planning system.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2018

Generalized Jacobi method for linear bounded operators system

In this paper, we construct a generalization of the Jacobi iterative method adapted to a system of linear bounded operators. This new method is used with product integration method to solve a linear Fredholm integral equation of the second kind with a weakly singular kernel. The convergence analysis is proved. The numerical tests developed show its effectiveness.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A method to predict texture effect on ion beam channeling analysis of polycrystals and the application to study the mosaic spreading effect in highly oriented pyrolytic graphite

We propose a method to convert the channeling Rutherford backscattering spectrum yield map of a single crystal to a polycrystal through a matrix rotation technique. The rotation matrix is determined by the deviation of the crystal axial direction from the original z axis. The final yield map is created after averaging the rotated yields using the texture function as the weight factor. For highly oriented pyrolytic graphite (HOPG) exhibiting mosaic spread, the method leads to a Gaussian kernel averaging of the map obtained from a single crystal. The yield map of a single crystal is obtained by a simulation of ion trajectories in a potential field described by Moliere screened Coulomb potentials. Yield maps are calculated under various σ values (standard deviations of mosaic spread). The simulated results are compared with experimental results obtained using 1.2 MeV alpha particle. σ is extracted through the best fitting, demonstrating that the method can be used to obtain texture details. The effects of mosaic spread on minimum yield χ min and the half-width at half maximum of angular scans ψ ½ are systematically modeled and compared with previous theoretical equations. The study also shows that previous theoretical equations are valid only at small σ values. The proposed method can be applied to any type of polycrystal and is not limited to HOPG. It provides near-surface mosaic spread and crystallography information with a longitudinal depth resolution of tens of nanometers and is not influenced by grain shapes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗