Plug and play: a general approach for the fusion of sensor and machine learning models
Regularized or Bayesian inversion has revolutionized our ability to reconstruct images from incomplete data.
97 MATHEMATICS AND COMPUTING↗
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Results for “Mathematics & Computing”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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NREL HPC FY23 Allocation Webinar
This is an overview of the EERE and NREL HPC allocation process designed to help users submit requests in an effective manner.
Eagle↗
SST ..kappa..-..omega.. Simulations of the Atmospheric Boundary Layer Including the Coriolis Effect
For large-scale structures in the atmospheric boundary layer (ABL), the Coriolis effect and near-wall behavior can have a meaningful impact. For example, both the Coriolis effect and blade boundary layer impact how muchpower wind farms produce. RANS simulations of the ABL typically use the ..kappa..-epsilon turbulence model, which has been developed to accurately capture the Coriolis effect but typically does not perform well near walls. The SST ..kappa..-..omega.. turbulence model performs well near walls but does not accurately capture the Coriolis effect. This work modifies SST ..kappa..-..omega.. to accurately model the Coriolis effect. We discuss the similarities and differences in how to modify ..kappa..-epsilon and SST ..kappa..-..omega.. for the Coriolis effect. Finally, we compare ..kappa..-epsilon and SST ..kappa..-..omega.. simulations of the ABL, including the Coriolis effect, with large eddy simulations and measurements.
atmospheric boundary layer↗
Green AI: Insights Into Deep Learning's Looming Energy Efficiency Crisis
As demands grow to integrate artificial intelligence into every aspect of industry, commerce, and life, deep learning's exploding energy cost has become a looming crisis, making AI systems a salient energy-efficiency challenge. One might expect that doubling a neural network's size would halve its error rate, or at least allow it to achieve greater performance given the same amount of time and energy. I will present clear and substantial scientific evidence which indicates that not only is this intuition wildly wrong, but that neural networks scale so poorly that to increase deep learning performance by only a small fraction can easily require an order of magnitude or more increase in computational resources and energy. Further, the marginal trade-off price of to increase model performance rapidly explodes as performance targets are increased. To address this challenge, I will provide a toolkit of techniques that can be applied today to mitigate the inefficiency of modern deep learning. And, I will conclude by illuminating a practical path forward towards efficient, Green AI.
artificial intelligence↗
Internal neutronics-temperature coupling in Serpent 2 - Reactivity differences resulting from choice of material property correlations
This paper describes the unique way of simultaneously solving the power and temperature distributions of a nuclear system with the Monte Carlo neutron transport code Serpent 2. The coupled solution is achieved through the implementation of an internal temperature solver and material property correlations in the code. The program structure is reviewed concerning the temperature solver and the internal correlations as well as the internal coupling between these two and the neutron transport part. To estimate the reactivity differences resulting from correlation choices a simple pin-cell case has been calculated. It is established, that some correlation choices may result in difference in reactivity of approximately 100 pcm. (authors)
97 MATHEMATICS AND COMPUTING↗
Proteus-MOC: A 3D deterministic solver incorporating 2D method of characteristics
A new transport solution methodology was developed by combining the two-dimensional method of characteristics with the discontinuous Galerkin method for the treatment of the axial variable. The method, which can be applied to arbitrary extruded geometries, was implemented in PROTEUS-MOC and includes parallelization in group, angle, plane, and space using a top level GMRES linear algebra solver. Verification tests were performed to show accuracy and stability of the method with the increased number of angular directions and mesh elements. Good scalability with parallelism in angle and axial planes is displayed. (authors)
97 MATHEMATICS AND COMPUTING↗
Decision Points and Practical Considerations for AI Projects
In this presentation, I will present business-relevant decisions, risks, and considerations for practical implementations of AI projects. I will use energy efficiency and renewable energy AI projects at NREL as examples and case-studies highlighting the journey from concept to implementation. First, I present challenges, questions, and trade-offs related to system inputs: the data. Next, I will examine issues with system behavior and trust, presenting examples, risks, and mitigation strategies. Finally, I will discuss challenges to effective widespread deployment of AI systems including energy, compute, and time requirements.
AI↗
Simulating Microbial Community Patterning Using Biocellion
Mathematical modeling and computer simulation are important tools for understanding complex interactions between cells and their biotic and abiotic environment: similarities and differences between modeled and observed behavior provide the basis for hypothesis forma- tion. Momeni et al. [5] investigated pattern formation in communities of yeast strains engaging in different types of ecological interactions, comparing the predictions of mathematical modeling and simulation to actual patterns observed in wet-lab experiments. However, simu- lations of millions of cells in a three-dimensional community are ex- tremely time-consuming. One simulation run in MATLAB may take a week or longer, inhibiting exploration of the vast space of parameter combinations and assumptions. Improving the speed, scale, and accu- racy of such simulations facilitates hypothesis formation and expedites discovery. Biocellion is a high performance software framework for ac- celerating discrete agent-based simulation of biological systems with millions to trillions of cells. Simulations of comparable scale and accu- racy to those taking a week of computer time using MATLAB require just hours using Biocellion on a multicore workstation. Biocellion fur- ther accelerates large scale, high resolution simulations using cluster computers by partitioning the work to run on multiple compute nodes. Biocellion targets computational biologists who have mathematical modeling backgrounds and basic C++ programming skills. This chap- ter describes the necessary steps to adapt the original Momeni et al.'s model to the Biocellion framework as a case study.
metabolic interaction↗
A micro-computer based system to compute magnetic variation
A mathematical model of magnetic variation in the continental United States (COT48) was implemented in the Ohio University LORAN C receiver. The model is based on a least squares fit of a polynomial function. The implementation on the microprocessor based LORAN C receiver is possible with the help of a math chip, Am9511 which performs 32 bit floating point mathematical operations. A Peripheral Interface Adapter (M6520) is used to communicate between the 6502 based micro-computer and the 9511 math chip. The implementation provides magnetic variation data to the pilot as a function of latitude and longitude. The model and the real time implementation in the receiver are described.
Kaul, R.↗
Computationally Efficient Training of Deep Neural Networks via Transfer Learning
Transfer learning is a highly successful approach to train deep neural networks for customized image recognition tasks. Transfer learning leverages deep learning models that are previously trained on massive datasets and re-trains the network for a novel image recognition dataset. Typically, the advantage of transfer learning has been measured in sample efficiency, but instead, we investigate the computational efficiency of transfer learning. A good pre-trained model provides features that can be used as input to a new classifier (usually the top layers of a neural network). We show that if a good pre-trained model is selected, that training a new classifier can be much more computationally efficient than training a deep neural network without transfer learning. The first step in transfer learning is to select a pre-trained model to use as a feed-forward network for generating features. Here this selection process either uses human intuition/convenience or a methodical but computationally intensive validation loop. Instead, we would prefer a method to select the pre-trained model that will produce the best transfer results for the least amount of computation. To this end, we provide a computationally efficient metric for the fit between a pre-trained model and a novel image recognition task. The better the fit, the less computation will be needed to re-train the pre-trained model for the novel task. As machine learning becomes ubiquitous, highly-accurate trained models will proliferate and computationally efficient transfer learning methods will enable rapid development of new image recognition models.
97 MATHEMATICS AND COMPUTING↗
Force Reconstruction Using the Inverse of the Mode-Shape Matrix [Book Chapter]
A new technique for force reconstruction is developed. To estimate the externally applied force, this technique sums the weight-scaled acceleration signals, and is referred to as the Sum of Weighted Accelerations Technique (SWAT). To obtain the scalar weights the inverse of the mode shape matrix is used. Application of this technique is illustrated with both numerical calculations using a mass-spring model and experimental data from a structure impacting a rigid barrier.
055001 -- Nuclear Fuels-- Safeguards, Inspection, ↗
Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model
The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.
59 BASIC BIOLOGICAL SCIENCES↗
A theory of supercritical wing sections, with computer programs and examples.
Mathematical methods for the design of supercritical wings, which depend on the numerical solution of the partial differential equations of two-dimensional gas dynamics, are developed. The main contribution is a computer program for the design of shockless transonic airfoils using the hodograph transformation and analytic continuation into the complex domain. The mathematical theory is described, and a manual for users of the programs is provided. Numerical examples are given and computational results are discussed, and the computer programs themselves are listed. The analysis routine can be used to ascertain whether the profiles behave well at off-design conditions, or to smooth coordinates and obtain a desirable shape more quickly when perfectly shockless flow is not essential.
Bauer, F.↗
Numerical and Analytical Analysis of Thin Laser-Driven Flyer Plates
Computational and analytical investigations have been performed for laser-driven flyer plate experiments and compared with data. These have resulted in a more fundamental understanding of the physical processes in the laser absorption, and acceleration of the flyers by the expansion of laser produced plasma. The analytical work describes the dependences of final foil velocity, while the computational simulations permit a detailed look at energy coupling and foil acceleration issues.
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
Computer program for prediction of heat transfer through glass.
Thermal behavior of space vehicle window systems predicted by mathematical analysis and computer methods for heat transfer through glass
Comstock, D. F.↗
Higher-order LaSDI: Reduced order modeling with multiple time derivatives
Solving complex partial differential equations (PDEs) is essential across scientific disciplines but often requires numerical models that can be prohibitively expensive in time-sensitive applications. Reduced-order models (ROMs) address this challenge by exploiting low-dimensional structure to create fast approximations. The Latent Space Dynamics Identification (LaSDI) framework has demonstrated success in learning ROMs for parameterized PDE families, but remains limited to first-order systems. Here, in this paper, we propose Higher-Order LaSDI (HLaSDI), which extends the LaSDI framework to PDEs with arbitrary order of time derivatives. This generalization significantly expands the applicability of LaSDI-based methods to systems previously outside their scope, including hyperbolic PDEs. We demonstrate HLaSDI’s accuracy and efficiency on several linear and nonlinear benchmark problems.
97 MATHEMATICS AND COMPUTING↗
Accurate real space iterative reconstruction (RESIRE) algorithm for tomography
Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at https://zenodo.org/record/7273314.
97 MATHEMATICS AND COMPUTING↗
A comparison of machine learning methods to classify radioactive elements using prompt-gamma-ray neutron activation data
The detection of illicit radiological materials is critical to establishing a robust second line of defence in nuclear security. Neutron-capture prompt-gamma activation analysis (PGAA) can be used to detect multiple radioactive materials across the entire Periodic Table. However, long detection times and a high rate of false positives pose a significant hindrance in the deployment of PGAA-based systems to identify the presence of illicit substances in nuclear forensics. In the present work, six different machine-learning algorithms were developed to classify radioactive elements based on the PGAA energy spectra. The model performance was evaluated using standard classification metrics and trend curves with an emphasis on comparing the effectiveness of algorithms that are best suited for classifying imbalanced datasets. We analyse the classification performance based on Precision, Recall, F1-score, Specificity, Confusion matrix, ROC-AUC curves, and Geometric Mean Score (GMS) measures. The tree-based algorithms (Decision Trees, Random Forest and AdaBoost) have consistently outperformed Support Vector Machine and K-Nearest Neighbours. Based on the results presented, AdaBoost is the preferred classifier to analyse data containing PGAA spectral information due to the high recall and minimal false negatives reported in the minority class.
97 MATHEMATICS AND COMPUTING↗