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At least 109 records · Page 6

Real-Time Radiological Source Term Estimation for Multiple Sources in Cluttered Environments

A particle filter algorithm is presented to estimate the position, strength, and cardinality of an unknown number of radioactive point sources in an obstacle-rich environment using count measurements. The algorithm addresses gaps in the prior literature by incorporating two novel elements. The first is a precomputation step in which local terrain and obstacle data is processed to compute attenuation kernels throughout the search area. This enables rapid estimation performance in obstacle-rich environments as measurements are gathered. The second novel feature is a dynamic particle allocation technique in which the number of particles is adjusted in real time to meet convergence goals. This feature allows the algorithm to scale more efficiently to scenarios with a larger number of sources. Furthermore, a series of computational experiments using simulated data demonstrates the algorithm’s performance in a cluttered environment with up to eight sources.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

EUCLID: Experiments Underpinned by Computational Learning for Improvements in Nuclear Data [Slides]

EUCLID will design validation experiments optimized to resolve compensating errors and adjust nuclear data to experiments. A big part of the success of the EUCLID proposal was due to previous work supported by NCSP (MCNP, nuclear data, and NCERC capabilities). The work performed under EUCLID will similarly benefit the NCSP mission. It will lead to new MCNP capabilities, improved nuclear data and nuclear data capabilities, and new methodology and tools that will have large impact on future NCERC experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Discovering Active Subspaces for High-Dimensional Computer Models

Dimension reduction techniques have long been an important topic in statistics, and active subspaces (AS) have received much attention this past decade in the computer experiments literature. The most common approach towards estimating the AS is to use Monte Carlo with numerical gradient evaluation. While sensible in some settings, this approach has obvious drawbacks. Recent research has demonstrated that active subspace calculations can be obtained in closed form, conditional on a Gaussian process (GP) surrogate, which can be limiting in high-dimensional settings for computational reasons. In this paper, we produce the relevant calculations for a more general case when the model of interest is a linear combination of tensor products. These general equations can be applied to the GP, recovering previous results as a special case, or applied to the models constructed by other regression techniques including multivariate adaptive regression splines (MARS). Furthermore, using a MARS surrogate has many advantages including improved scaling, better estimation of active subspaces in high dimensions and the ability to handle a large number of prior distributions in closed form. In one real-world example, we obtain the active subspace of a radiation-transport code with 240 inputs and 9,372 model runs in under half an hour.

97 MATHEMATICS AND COMPUTING↗

Gemma V&V/UQ/Credibility Activities: FY2020 Progress

This report describes the credibility activities undertaken in support of Gemma code development in FY20, which include Verification & Validation (V&V), Uncertainty Quantification (UQ), and Credibility process application. The main goal of these activities is to establish capabilities and process frameworks that can be more broadly applied to new and more advanced problems as the Gemma code development effort matures. This will provide Gemma developers and analysts with the tools needed to generate credibility evidence in support of Gemma predictions for future use cases. The FY20 Gemma V&V/UQ/Credibility activities described in this report include experimental uncertainty analysis, the development and use of methods for optimal design of computer experiments, and the development of a framework for validation. These initial activities supported the development of broader credibility planning for Gemma that continued into FY21.

97 MATHEMATICS AND COMPUTING↗

Comparison of open‐source three‐dimensional reconstruction pipelines for maize‐root phenotyping

Abstract Understanding three‐dimensional (3D) root traits is essential to improve water uptake, increase nitrogen capture, and raise carbon sequestration from the atmosphere. However, quantifying 3D root traits by reconstructing 3D root models for deeper field‐grown roots remains a challenge due to the unknown tradeoff between 3D root‐model quality and 3D root‐trait accuracy. Therefore, we performed two computational experiments. We first compared the 3D model quality generated by five state‐of‐the‐art open‐source 3D model reconstruction pipelines on 12 contrasting genotypes of field‐grown maize roots. These pipelines included COLMAP, COLMAP+PMVS (Patch‐based Multi‐View Stereo), VisualSFM, Meshroom, and OpenMVG+MVE (Multi‐View Environment). The COLMAP pipeline achieved the best performance regarding 3D model quality versus computational time and image number needed. In the second test, we compared the accuracy of 3D root‐trait measurement generated by the Digital Imaging of Root Traits 3D pipeline (DIRT/3D) using COLMAP‐based 3D reconstruction with our current DIRT/3D pipeline that uses a VisualSFM‐based 3D reconstruction on the same dataset of 12 genotypes, with 5–10 replicates per genotype. The results revealed that (1) the average number of images needed to build a denser 3D model was reduced from 3000 to 3600 (DIRT/3D [VisualSFM‐based 3D reconstruction]) to around 360 for computational test 1, and around 600 for computational test 2 (DIRT/3D [COLMAP‐based 3D reconstruction]); (2) denser 3D models helped improve the accuracy of the 3D root‐trait measurement; (3) reducing the number of images can help resolve data storage problems. The updated DIRT/3D (COLMAP‐based 3D reconstruction) pipeline enables quicker image collection without compromising the accuracy of 3D root‐trait measurements.

09 BIOMASS FUELS↗

Multi-stage heat release of multi-component fuels: Insights and implications for advanced engine operation

Multi-stage heat release (MSHR) is a unique phenomenon typically seen in lean/diluted and low- to intermediate-temperature combustion. Despite its relevance to advanced engine operation, the MSHR of multi-component fuels has barely been quantified. This study aims to characterize the MSHR of multi-component fuels in a rapid compression machine (RCM) at conditions representative of advanced combustion engines. New experimental data are first reported in the RCM at an equivalence ratio of 0.4, pressure of 60 bar and temperatures from 702 to 795 K for a research grade, multi-component gasoline surrogate, termed PACE-20. Here, experiments confirm the existence of MSHR for PACE-20 at all temperatures, and reveal the strong inhibiting effect of temperature on MSHR, where increasing temperature inhibits MSHR by suppressing first stage heat release and promoting second and third stage heat release. A detailed chemical kinetic model is also adopted to model the experiments, with good agreement observed. The response of MSHR characteristics to changes in different engine operating parameters (i.e., temperature, pressure, equivalence ratio and CO 2 dilution level) and fuel compositions (i.e., mole fraction of n-pentane, n-heptane, isooctane, cyclopentane, 1-hexene, ethanol and aromatics in PACE-20) is further evaluated via statistical analysis coupling quasi-random sampling, extensive computer experiments and high-dimensional model representation. The change in MSHR is characterized through 8 quantities of interest (QOIs), i.e., duration and extent of each heat release stage, and their standard deviations. The analysis highlights the dependence of the QOIs on the individual parameters as well as their interplays, with temperature exhibiting the strongest impact among all parameters. Furthermore, it is demonstrated that if MSHR is to be facilitated and combustion phasing is to be extended to enable engine operation at higher compression ratios, it is recommended to operate the engine at low intake temperatures, boosted intake pressures and high CO 2 dilutions (i.e., high EGR levels) with gasoline fuels containing more n-pentane and less aromatics.

42 ENGINEERING↗

Motion Dynamics of Motile Microbes in Pore-Networks and its Implications for Reactive Transport Processes

This report outlines new methods to improve simulations of microbial transport and microbially mediated reactions in porous media. A range of experimental, modeling, and machine learning tools are introduced to make these simulations faster, more reliable, and useful for real-world applications. At the microscopic level, the study investigates how different types of bacteria move through confined spaces. A new artificial intelligence tool called DeepTrackStat, is introduced to track motions dynamics as observed in videos of particles migrating through pore networks. This tool is especially helpful for studying fast-moving microbes and requires less computing power than traditional tracking methods. At larger scales, the research looks at how microbes and chemicals interact in zones where surface water and groundwater meet. To connect the small- and large-scale findings, the study presents a neural network model called STAMNet. This tool helps scale up detailed small-scale microbial motion behaviors to predict large-scale environmental changes more efficiently. By combining lab experiments, computer models, and artificial intelligence, the research presented supports smarter environmental decision-making, especially in bioremediation of contaminated groundwater and protection of water quality.

54 ENVIRONMENTAL SCIENCES↗

Automatic Differentiation of C++ Codes on Emerging Manycore Architectures with Sacado

Automatic differentiation (AD) is a well-known technique for evaluating analytic derivatives of calculations implemented on a computer, with numerous software tools available for incorporating AD technology into complex applications. However, a growing challenge for AD is the efficient differentiation of parallel computations implemented on emerging manycore computing architectures such as multicore CPUs, GPUs, and accelerators as these devices become more pervasive. In this work, we explore forward mode, operator overloading-based differentiation of C++ codes on these architectures using the widely available Sacado AD software package. In particular, we leverage Kokkos, a C++ tool providing APIs for implementing parallel computations that is portable to a wide variety of emerging architectures. Here we describe the challenges that arise when differentiating code for these architectures using Kokkos, and two approaches for overcoming them that ensure optimal memory access patterns as well as expose additional dimensions of fine-grained parallelism in the derivative calculation. We describe the results of several computational experiments that demonstrate the performance of the approach on a few contemporary CPU and GPU architectures. We then conclude with applications of these techniques to the simulation of discretized systems of partial differential equations.

97 MATHEMATICS AND COMPUTING↗

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

Here we propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of constructing a very wide network while keeping the number of parameters low. Our theoretical analysis reveals that under suitable conditions, KNNs induce a faster decay of the loss than that by the feed-forward networks. This is also empirically verified through a set of computational examples. Furthermore, under certain technical assumptions, we establish global convergence of gradient descent for KNNs. As a specific case, we propose the Rowdy activation function that is designed to get rid of any saturation region by injecting sinusoidal fluctuations, which include trainable parameters. The proposed Rowdy activation function can be employed in any neural network architecture like feed-forward neural networks, Recurrent neural networks, Convolutional neural networks etc. The effectiveness of KNNs with Rowdy activation is demonstrated through various computational experiments including function approximation using feed-forward neural networks, solution inference of partial differential equations using the physics-informed neural networks, and standard deep learning benchmark problems using convolutional and fully-connected neural networks.

97 MATHEMATICS AND COMPUTING↗

A computational study of symmetry and well-posedness of structural topology optimization

We report on computational topological optimization of elastic structures, in particular minimization of compliance subject to a constraint on the mass. Through computational experiments, it is discovered that even very simple optimization problems can exhibit complex behavior such as critical points and bifurcation. In the vicinity of significant points, structural topology optimization problems are not well-posed since infinitesimally small perturbations lead to distinct topologies.

42 ENGINEERING↗

A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

We address the bilevel optimization problem of identifying the most critical attacks to an alternating current (AC) power flow network. The upper-level binary maximization problem consists of choosing an attack that is treated as a parameter in the lower-level defender minimization problem. Instances of the lower-level global minimization problem by themselves are NP-hard due to the nonconvex AC power flow constraints, and bilevel solution approaches commonly apply a convex relaxation or approximation to allow for tractable bilevel reformulations at the cost of underestimating some power system vulnerabilities. Our main contribution is to provide an alternative branch-and-bound algorithm whose upper bounding mechanism (in a maximization context) is based on a reformulation that avoids relaxation of the AC power flow constraints in the lower-level defender problem. Lower bounding is provided with semidefinite programming (SDP) relaxed solutions to the lower-level problem. We establish finite termination with guarantees of either a globally optimal solution to the original bilevel problem, or a globally optimal solution to the SDP-relaxed bilevel problem which is included in a vetted list of upper-level attack solutions, at least one of which is a globally optimal solution to the bilevel problem. We demonstrate through computational experiments applied to IEEE case instances both the relevance of our contribution, and the effectiveness of our contributed algorithm for identifying power system vulnerabilities without resorting to convex relaxations of the lower-level problem. We conclude with a discussion of future extensions and improvements.

97 MATHEMATICS AND COMPUTING↗

Surrogate Model Selection for Design Space Approximation And Surrogatebased Optimization

Surrogate models are used to map input data to output data when the actual relationship between the two is unknown or computationally expensive to evaluate for sensitivity analysis, uncertainty propagation and surrogate based optimization. This work evaluates the performance of eight surrogate modeling techniques for design space approximation and surrogate based optimization applications over a set of generated datasets with known characteristics. With this work, we aim to provide general rules for selecting an appropriate surrogate model form solely based on the characteristics of the data being modeled. Furthermore, the computational experiments revealed that, in general, multivariate adaptive regression spline models (MARS) and single hidden layer feed forward neural networks (ANN) yielded the most accurate predictions over the design space while Random Forest (RF) models most reliably identified the locations of the optimums when used for surrogate-based optimization.

97 MATHEMATICS AND COMPUTING↗

A novel low-rank matrix completion approach to estimate missing entries in Euclidean distance matrix

A Euclidean distance matrix (EDM) is a table of distance-square between points on a k-dimensional Euclidean space, with applications in many fields (e.g., engineering, geodesy, economics, genetics, biochemistry, and psychology). A problem that often arises is the absence (or uncertainty) of some EDM elements. In many situations, only a subset of all pairwise distances is available and it is desired to have some procedure to estimate the missing distances. In this paper, we address the problem of missing data in EDM through low-rank matrix completion techniques. We exploit the fact that the rank of a EDM is at most k+2 and does not depend on the number of points, which is, in general, much bigger then k. We use a singular value decomposition approach that considers the rank of the matrix to be completed and computes, in each iteration, a parameter that controls the convergence of the method. After performing a number of computational experiments, we could observe that our proposal was able to recover, with high precision, random EDMs with more than 1000 points and up to 98% of missing data in few minutes. In addition, our method required a smaller number of iterations when compared to other competitive state-of-art technique.

97 MATHEMATICS AND COMPUTING↗

Discovery of LaAlO 3 as an efficient catalyst for two-electron water electrolysis towards hydrogen peroxide

Electrochemical two-electron water oxidation reaction (2e-WOR) has drawn significant attention as a promising process to achieve the continuous on-site production of hydrogen peroxide (H 2 O 2 ). However, compared to the cathodic H 2 O 2 generation, the anodic 2e-WOR is more challenging to establish catalysts due to the severe oxidizing environment. In this study, we combine density functional theory (DFT) calculations with experiments to discover a stable and efficient perovskite catalyst for the anodic 2e-WOR. Our theoretical screening efforts identify LaAlO 3 perovskite as a stable, active, and selective candidate for catalyzing 2e-WOR. Our experimental results verify that LaAlO 3 achieves an overpotential of 510 mV at 10 mA cm -2 in 4 M K 2 CO 3 /KHCO 3 , lower than those of many reported metal oxide catalysts. In addition, LaAlO 3 maintains a stable H 2 O 2 Faradaic efficiency with only a 3% decrease after 3 h at 2.7 V vs. RHE. This computation-experiment synergistic approach introduces another effective direction to discover promising catalysts for the harsh anodic 2e-WOR towards H 2 O 2 .

08 HYDROGEN↗

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↗

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗

Efficiency of Uncertainty Propagation Methods for Estimating Output Moments

Uncertainty propagation methods are used to estimate the distribution of model outputs resulting from a set of uncertain model outputs. There are a number of uncertainty propagation methods available in literature. This paper compares six non-intrusive uncertainty propagation methods, Latin Hypercube Sampling, Full Factorial Integration, Univariate Dimension Reduction, Halton series, Sobol series, and Polynomial Chaos Expansion, in terms of their efficiency for estimating the first four moments of the output distribution using computational experiments. Here, the results suggest employing FFNI if there are few uncertain inputs, up to three. Uncertainty propagation methods that utilize Halton and Sobol series are found to be robust for estimating output moments as the number of uncertain inputs increases. In general, higher order polynomial chaos expansion approximations (3rd-5th order) obtained accurate estimates of model outputs with fewer model evaluations.

97 MATHEMATICS AND COMPUTING↗