Approximate Forest Completion and Learning-Augmented Algorithms for Metric Minimum Spanning Trees
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Hybrid programming-model strategies for GPU offloading of electronic structure calculation kernels
To address the challenge of performance portability and facilitate the implementation of electronic structure solvers, we developed the basic matrix library (BML) and Parallel, Rapid O(N), and Graph-based Recursive Electronic Structure Solver (PROGRESS) library. The BML implements linear algebra operations necessary for electronic structure kernels using a unified user interface for various matrix formats (dense and sparse) and architectures (CPUs and GPUs). Focusing on density functional theory and tight-binding models, PROGRESS implements several solvers for computing the single-particle density matrix and relies on BML. In this paper, we describe the general strategies used for these implementations on various computer architectures, using OpenMP target functionalities on GPUs, in conjunction with third-party libraries to handle performance critical numerical kernels. In this study, we demonstrate the portability of this approach and its performance in benchmark problems.
36 MATERIALS SCIENCE↗
Transforming Energy Through Computational Excellence: A View From NREL
At the National Renewable Energy Laboratory (NREL)—a U.S. Department of Energy laboratory—computational science, high-performance computing, applied mathematics, advanced computer science, visualization, and data play a pivotal role in advancing energy abundance, affordability, security, and reliability. From fundamental scientifc discovery to systems engineering and analysis, NREL researchers tackle market-relevant challenges to develop solutions for an independent energy system that is reliable, resilient and secure. Collaborative partnerships with industry, government, and academia ensure that our research remains cutting edge, impactful, applicable, and aligned with real-world energy needs. This special issue of Computing in Science & Engineering highlights exemplary NREL projects where computational tools and methodologies drive discovery and accelerate innovation in scalable and integrated energy systems. The featured articles explore the role of computational modeling, high-performance computing, generative AI, and adaptive computing in advancing independent energy solutions, optimizing sustainability research, and enhancing decision-making for energy solutions using a broad mix of energy technologies. Here, these contributions demonstrate how NREL’s computational research bridges the gap between theoretical advancements and practical implementation, emphasizing interdisciplinary collaboration and a commitment to innovation, with a focus on translating computational excellence into real-world impact, thus accelerate progress toward national energy goals. By showcasing cutting-edge research at the intersection of computational science and energy systems, this issue aims to inspire and inform researchers, practitioners, and policymakers dedicated to shaping a more reliable energy future.
97 MATHEMATICS AND COMPUTING↗
AI-based design of a nuclear reactor core
The authors developed an artificial intelligence (AI)-based algorithm for the design and optimization of a nuclear reactor core based on a flexible geometry and demonstrated a 3× improvement in the selected performance metric: temperature peaking factor. The rapid development of advanced, and specifically, additive manufacturing (3-D printing) and its introduction into advanced nuclear core design through the Transformational Challenge Reactor program have presented the opportunity to explore the arbitrary geometry design of nuclear-heated structures. The primary challenge is that the arbitrary geometry design space is vast and requires the computational evaluation of many candidate designs, and the multiphysics simulation of nuclear systems is very time-intensive. Therefore, the authors developed a machine learning-based multiphysics emulator and evaluated thousands of candidate geometries on Summit, Oak Ridge National Laboratory’s leadership class supercomputer. The results presented in this work demonstrate temperature distribution smoothing in a nuclear reactor core through the manipulation of the geometry, which is traditionally achieved in light water reactors through variable assembly loading in the axial direction and fuel shuffling during refueling in the radial direction. The conclusions discuss the future implications for nuclear systems design with arbitrary geometry and the potential for AI-based autonomous design algorithms.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions
It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Benchmarking the performance of uncertainty quantification methods for neural network-based interatomic potentials
Machine-learned interatomic potentials (ML-IAPs) continue to gain popularity as accurate, computationally efficient replacements for traditional, physics-based interatomic potentials and expensive ab initio methods. Uncertainty quantification (UQ) of ML-IAPs is a growing area of research as UQ is critical in many applications of IAPs, such as developing curated datasets, active learning-based data augmentation, self-improving models, and estimating the uncertainty of molecular dynamics simulations. In this paper, we construct and benchmark a series of different neural network potentials (NNPs) with varying network architectures to determine the performance of these models with respect to both the mean and uncertainty calibration error. Each NNP method is specifically designed to predict either epistemic or aleatoric uncertainty with particular focus on the differences in behavior between the epistemic and aleatoric uncertainty estimates. We benchmark these methods using multiple datasets common in the ML-IAP literature. The results show that the aleatoric uncertainty from single-shot model architectures is a competitive alternative to ensemble-based epistemic uncertainty predictions in regions of sufficient data-density. However, in regions where the representative data is sparse, aleatoric uncertainty models tend to overpredict and epistemic methods tend to underpredict the actual model error. We conclude that the type of UQ is crucial when discussing performance of probabilistic model results as different methods have different performance characteristics depending on the regime in which they are evaluated. Therefore, the type of UQ method should be carefully evaluated against both the data characteristics and requirements for the intended application.
97 MATHEMATICS AND COMPUTING↗
Deep learning with mixup augmentation for improved pore detection during additive manufacturing
In additive manufacturing (AM), process defects such as keyhole pores are difficult to anticipate, affecting the quality and integrity of the AM-produced materials. Hence, considerable efforts have aimed to predict these process defects by training machine learning (ML) models using passive measurements such as acoustic emissions. This work considered a dataset in which keyhole pores of a laser powder bed fusion (LPBF) experiment were identified using X-ray radiography and then registered both in space and time to acoustic measurements recorded during the LPBF experiment. Due to AM’s intrinsic process controls, where a pore-forming event is relatively rare, the acoustic datasets collected during monitoring include more non-pores than pores. In other words, the dataset for ML model development is imbalanced. Moreover, this imbalanced and sparse data phenomenon remains ubiquitous across many AM monitoring schemes since training data is nontrivial to collect. Hence, we propose a machine learning approach to improve this dataset imbalance and enhance the prediction accuracy of pore-labeled data. Specifically, we investigate how data augmentation helps predict pores and non-pores better. This imbalance is improved using recent advances in data augmentation called Mixup, a weak-supervised learning method. Convolutional neural networks (CNNs) are trained on original and augmented datasets, and an appreciable increase in performance is reported when testing on five different experimental trials. When ML models are trained on original and augmented datasets, they achieve an accuracy of 95% and 99% on test datasets, respectively. We also provide information on how dataset size affects model performance. Lastly, we investigate the optimal Mixup parameters for augmentation in the context of CNN performance.
36 MATERIALS SCIENCE↗
Reinforcement learning for block decomposition of planar CAD models
Abstract The problem of hexahedral mesh generation of general CAD models has vexed researchers for over 3 decades and analysts often spend more than 50% of the design-analysis cycle time decomposing complex models into simpler blocks meshable by existing techniques. The decomposed blocks are required for generating good quality meshes (tilings of quadrilaterals or hexahedra) suitable for numerical simulations of physical systems governed by conservation laws. We present a novel AI-assisted method for decomposing (segmenting) planar CAD (computer-aided design) models into well shaped rectangular blocks. Even though the simple examples presented here can also be meshed using many conventional methods, we believe this work is proof-of-principle of a AI-based decomposition method that can eventually be generalized to complex 2D and 3D CAD models. Our method uses reinforcement learning to train an agent to perform a series of optimal cuts on the CAD model that result in a good quality block decomposition. We show that the agent quickly learns an effective strategy for picking the location and direction of the cuts and maximizing its rewards. This paper is the first successful demonstration of an agent autonomously learning how to perform this block decomposition task effectively, thereby holding the promise of a viable method to automate this challenging process for more complex cases.
97 MATHEMATICS AND COMPUTING↗
A phase transition for finding needles in nonlinear haystacks with LASSO artificial neural networks
To fit sparse linear associations, a LASSO sparsity inducing penalty with a single hyperparameter provably allows to recover the important features (needles) with high probability in certain regimes even if the sample size is smaller than the dimension of the input vector (haystack). More recently learners known as artificial neural networks (ANN) have shown great successes in many machine learning tasks, in particular fitting nonlinear associations. Small learning rate, stochastic gradient descent algorithm and large training set help to cope with the explosion in the number of parameters present in deep neural networks. Yet few ANN learners have been developed and studied to find needles in nonlinear haystacks. Driven by a single hyperparameter, our ANN learner, like for sparse linear associations, exhibits a phase transition in the probability of retrieving the needles, which we do not observe with other ANN learners. To select our penalty parameter, we generalize the universal threshold of Donoho and Johnstone (Biometrika 81(3):425–455, 1994) which is a better rule than the conservative (too many false detections) and expensive cross-validation. In the spirit of simulated annealing, we propose a warm-start sparsity inducing algorithm to solve the high-dimensional, non-convex and non-differentiable optimization problem. We perform simulated and real data Monte Carlo experiments to quantify the effectiveness of our approach.
97 MATHEMATICS AND COMPUTING↗
Summary of research in applied mathematics, numerical analysis, and computer sciences
The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.
Source record↗
NASA Aeronautics Multidisciplinary Analysis and Design Fellowship Program
For a number of years, Virginia Tech had been on the forefront of research in the area of multidisciplinary analysis and design. In June of 1994, faculty members from aerospace and ocean engineering, engineering science and mechanics, mechanical engineering, industrial engineering, mathematics and computer sciences, at Virginia Tech joined together to form the Multidisciplinary Analysis and Design (MAD) Center for Advanced Vehicles. The center was established with the single goal: to perform research that is relevant to the needs of the US industry and to foster collaboration between the university, government and industry. In October of 1994, the center was chosen by NASA headquarters as one of the five university centers to establish a fellowship program to develop a graduate program in multidisciplinary analysis and design. The fellowship program provides full stipend and tuition support for seven U. S. students per year during their graduate studies. To advise us regarding the problems faced by the industry, an industrial advisory board has been formed consisting of representatives from industry as well as government laboratories. The function of the advisory board is to channel information from its member companies to faculty members concerning problems that need research attention in the general area of multidisciplinary design optimization (MDO). The faculty and their graduate students make proposals to the board on how to address these problems. At the annual board meeting in Blacksburg, the board discusses the proposals and suggests which students get funded under the NASA fellowship program. All students participating in the program are required to spend 3-6 months in industry working on their research projects. We are completing the third year of the fellowship program and have had three advisory board meetings in Blacksburg.
Grossman, B.↗
NASA Aeronautics Multidisciplinary Analysis and Design Fellowship Program
This program began as a grant from NASA Headquarters, NGT-10025, which was in effect from 10/l/93 until 10/31/96. The remaining funding for this effort was transferred from NASA Headquarters to NASA Langley and a new grant NGT-1-52155 was issued covering the period II/l/96 to 5/15/99. This report serves as the final report of NGT-1-52155. For a number of years, Virginia Tech had been on the forefront of research in the area of multidisciplinary analysis and design. In June of 1994, faculty members from aerospace and ocean engineering, engineering science and mechanics, mechanical engineering, industrial engineering, mathematics and computer sciences, at Virginia Tech joined together to form the Multidisciplinary Analysis and Design (MAD) Center for Advanced Vehicles. The center was established with the single goal: to perform research that is relevant to the needs of the US industry and to foster collaboration between the university, government and industry. In October of 1994, the center was chosen by NASA headquarters as one of the five university centers to establish a fellowship program to develop a graduate program in multidisciplinary analysis and design. The fellowship program provides full stipend and tuition support for seven U. S. students per year during their graduate studies. The grant is currently being administered by the NMO Branch of NASA Langley. To advise us regarding the problems faced by the industry, an industrial advisory board has been formed consisting of representatives from industry as well as government laboratories. The present membership includes major aerospace companies: Aurora Flight Sciences, Boeing: Philadelphia, Boeing: Long Beach, Boeing: Seattle, Boeing: St. Louis, Cessna, Ford, General Electric, Hughes, Lockheed-Martin: Palo Alto, Northrop-Grumman, Sikorsky, smaller, aerospace software companies: Aerosoft, Phoenix Integration and Proteus Engineering, along with representatives from government agencies, including: NASA Ames, Langley and Lewis. The function of the advisory board is to channel information from its member companies to faculty members concerning problems that need research attention in the general area of multidisciplinary design optimization (MDO). The faculty and their graduate students make presentations to the board on their research. The board makes recommendations on the research and suggests new areas and problems which need attention. Many students participating in the program spend 3-6 months in industry working on their research projects. We are completing the fifth year of the fellowship program and have had four advisory board meetings in Blacksburg. Ten students have spent the three month periods in industry. In addition to the research element of the MAD Center efforts we also have an academic component. We have developed a menu of design-related graduate courses and two new courses: one in Aerospace Manufacturing and another in MDO. Some of the MAD Center activities are described on the world-wide web at http://www.aoe.vt.edu/mads.html The MAD Center represents an innovative approach for joint Industry-Government-University cooperation in the development of a comprehensive program in engineering education which addresses the design needs of industry. The following charts list detail of the grant: mission of the MAD center, faculty members, purpose of the advisory board, board members, summary of the graduate and undergraduate program, history of the fellowship program, mission of the fellowship program, requirements of MAD fellows, course requirements, students supported, advisory board participants, and MAD center research papers
Grossman, B.↗
Models and Methods for Sparse (Hyper)Network Science in Business, Industry, and Government
The authors are hosting an AMS sponsored Mathematics Research Community (MRC) focusing on two themes that have garnered intense attention in network models of complex relational data: (1) how to faithfully model multi-way relations in hypergraphs, rather than only pairwise interactions in graphs; and (2) challenges posed by modelling networks with extreme sparsity. Here we introduce and explore these two themes and their challenges. In this work, we hope to generate interest from researchers in pure and applied mathematics and computer science.
97 MATHEMATICS AND COMPUTING↗
NASA Tech Briefs, February 2000
Topics covered include: Test and Measurement; Computer-Aided Design and Engineering; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Bio-Medical; Mathematics and Information Sciences; Computers and Peripherals.
Source record↗
Information-incorporated gene network construction with FDR control
Abstract Motivation Large-scale gene expression studies allow gene network construction to uncover associations among genes. To study direct associations among genes, partial correlation-based networks are preferred over marginal correlations. However, FDR control for partial correlation-based network construction is not well-studied. In addition, currently available partial correlation-based methods cannot take existing biological knowledge to help network construction while controlling FDR. Results In this paper, we propose a method called Partial Correlation Graph with Information Incorporation (PCGII). PCGII estimates partial correlations between each pair of genes by regularized node-wise regression that can incorporate prior knowledge while controlling the effects of all other genes. It handles high-dimensional data where the number of genes can be much larger than the sample size and controls FDR at the same time. We compare PCGII with several existing approaches through extensive simulation studies and demonstrate that PCGII has better FDR control and higher power. We apply PCGII to a plant gene expression dataset where it recovers confirmed regulatory relationships and a hub node, as well as several direct associations that shed light on potential functional relationships in the system. We also introduce a method to supplement observed data with a pseudogene to apply PCGII when no prior information is available, which also allows checking FDR control and power for real data analysis. Availability and implementation R package is freely available for download at https://cran.r-project.org/package=PCGII.
59 BASIC BIOLOGICAL SCIENCES↗
Challenges of COVID-19 Case Forecasting in the US, 2020–2021
During the COVID-19 pandemic, forecasting COVID-19 trends to support planning and response was a priority for scientists and decision makers alike. In the United States, COVID-19 forecasting was coordinated by a large group of universities, companies, and government entities led by the Centers for Disease Control and Prevention and the US COVID-19 Forecast Hub ( https://covid19forecasthub.org ). We evaluated approximately 9.7 million forecasts of weekly state-level COVID-19 cases for predictions 1–4 weeks into the future submitted by 24 teams from August 2020 to December 2021. We assessed coverage of central prediction intervals and weighted interval scores (WIS), adjusting for missing forecasts relative to a baseline forecast, and used a Gaussian generalized estimating equation (GEE) model to evaluate differences in skill across epidemic phases that were defined by the effective reproduction number. Overall, we found high variation in skill across individual models, with ensemble-based forecasts outperforming other approaches. Forecast skill relative to the baseline was generally higher for larger jurisdictions (e.g., states compared to counties). Over time, forecasts generally performed worst in periods of rapid changes in reported cases (either in increasing or decreasing epidemic phases) with 95% prediction interval coverage dropping below 50% during the growth phases of the winter 2020, Delta, and Omicron waves. Ideally, case forecasts could serve as a leading indicator of changes in transmission dynamics. However, while most COVID-19 case forecasts outperformed a naïve baseline model, even the most accurate case forecasts were unreliable in key phases. Further research could improve forecasts of leading indicators, like COVID-19 cases, by leveraging additional real-time data, addressing performance across phases, improving the characterization of forecast confidence, and ensuring that forecasts were coherent across spatial scales. In the meantime, it is critical for forecast users to appreciate current limitations and use a broad set of indicators to inform pandemic-related decision making.
59 BASIC BIOLOGICAL SCIENCES↗
An innovative data aggregation approach for assessing mosquito-borne disease risk [Slides]
Abstract not provided.
59 BASIC BIOLOGICAL SCIENCES↗
Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas
Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.
97 MATHEMATICS AND COMPUTING↗