Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical 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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analog Computing for Science

Conventional digital computing faces fundamental physical limits: large scale computing systems already con sume tens of Megawatts of power, Dennard scaling has ended, and data movement costs dominate application performance. Next generation experimental facilities generate data at rates that overwhelm conventional pro cessing and demand real-time analysis at the source. Analog computing, which exploits the continuous dynamics of physical systems to perform computation, promises a transformative path toward orders-of-magnitude gains in energy efficiency and time-to-solution for scientific workloads.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Determining the Axes of a Range-Doppler Image

Synthetic aperture radar (SAR) images formed with dechirp-on-receive data collection and rectangular format processing algorithm are the result of a two-dimensional discrete Fourier transform (DFT) applied to sampled data. There are several steps required to compute the range and Doppler values associated with each pixel in a SAR range-Doppler image. This memo walks readers through the process.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2024

Multiphysics Degradation Modeling of Energy Storage Materials via RKPM with a Neural Network-Enhancement

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation is developed, and a patch-test is formulated to certify optimal convergence of the proposed RKPM method for the coupled physics system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is then used to represent the complex material microstructures for modeling the coupled physics of these systems. Further, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

electro-chemo-mechanical coupling↗
DOE OSTI2025

Advanced Computing Annual Report 2024

In fiscal year (FY) 2024, the National Renewable Energy Laboratory (NREL) took a major leap forward with the completed full buildout of Kestrel, the Office of Energy Efficiency and Renewable Energy's newest high-performance computing (HPC) system. Kestrel is already supporting science across the portfolio, bringing roughly 44 petaflops of computing power, which is more than five times the capacity of our previous supercomputer, Eagle. By delivering greater GPU capacity, Kestrel enables faster progress in artificial intelligence (AI) and opens new avenues in energy research - from defining long-term planning scenarios to accommodate a growing power system to material discovery to improving energy efficiency in photovoltaics (PV). Across the portfolio, research is being accelerated by Kestrel's impressive power. During FY24, 427 projects and more than 700 researchers used NREL's HPC, supporting the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy across 13 funding areas. Through these collaborations, researchers produced more than 450 technical outputs, including 195 articles in peer-reviewed publications, pushing the boundaries of science and engineering. This year's report features new sections spotlighting the expanding roles of Artificial Intelligence and Accelerated Computing. We also introduce an early career section to celebrate the accomplishments of our up-and-coming researchers, whose pioneering work is shaping the future of energy. We hope you enjoy the new insights and discoveries highlighted in these pages.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Tensor network representation of non-abelian gauge theory coupled to reduced staggered fermions

We show how to construct a tensor network representation of the path integral for reduced staggered fermions coupled to a non-abelian gauge field in two dimensions. The resulting formulation is both memory and computation efficient because reduced staggered fermions can be represented in terms of a minimal number of tensor indices while the gauge sector can be approximated using Gaussian quadrature with a truncation. Numerical results obtained using the Grassmann TRG algorithm are shown for the case of SU(2) lattice gauge theory and compared to Monte Carlo results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

SOMA: Observability, monitoring, and in situ analytics for exascale applications

With the rise of exascale systems and large, data-centric workflows, the need to observe and analyze high performance computing (HPC) applications during their execution is becoming increasingly important. HPC applications are typically not designed with online monitoring in mind, therefore, the observability challenge lies in being able to access and analyze interesting events with low overhead while seamlessly integrating such capabilities into existing and new applications. We explore how our service-based observation, monitoring, and analytics (SOMA) approach to collecting and aggregating both application-specific diagnostic data and performance data addresses these needs. Furthermore, we present our SOMA framework and demonstrate its viability with LULESH, a hydrodynamics proxy application. Then we focus on Astaroth, a multi-GPU library for stencil computations, highlighting the integration of the TAU and APEX performance tools and SOMA for application and performance data monitoring.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Gaussian FLOWERS: Wind-rose-based analytical integration of Gaussian wake model for extremely fast AEP estimation

A major cost in the study of wind farm layout optimization is the repeated evaluation of the annual energy production (AEP). The current approach to estimating AEP requires a large set of flow simulations to be performed that cover each discrete wind speed and direction combination contained within the wind rose, followed by a probability-weighted sum of the power production resulting from each simulation. Even with inexpensive engineering wake models, this numerical integration scheme can lead to high computational costs. In this paper, we derive an analytical formulation for estimating farm AEP across every wind direction, based on a Gaussian wake velocity model, which reduces the number of wind farm simulations to a single function evaluation. As a result, we find that the Gaussian-FLOWERS approach reduces the time for AEP calculations by more than two orders of magnitude with a small trade-off in accuracy when compared to a conventional approach. This massive reduction in computation cost is useful to reduce overall costs in wind farm layout optimization studies.

17 WIND ENERGY↗
DOE OSTI2024

Unifying Combinatorial and Graphical Methods in Artificial Intelligence

Recently, a new graph Laplacian, called the inner product Laplacian, was introduced which generalizes many existing Laplacians, including the normalized and combinatorial Laplacian and their weighted variants. The key observation behind the inner product Laplacian is that by defining appropriate inner product spaces on the vertices and edges, the standard Laplacians can be recovered as Hodge Laplacians over the simplicial complex formed by the edges and vertices. These inner product spaces form a natural way to incorporate non-combinatorial information into the definition of a domain-specific Laplacian. In particular, in contrast to current domain-specific weighting schemes which rely solely on edge weights, information regarding the similarity of non-adjacent vertices and arbitrary pairs of edges can be effectively incorporated into the Laplacian. In order to illustrate this approach we consider the problem of calculating the potential energy of an atomistic configuration using Graph Neural Networks. In comparison with start-of-the-art approaches, such as SchNet, our approach replaces a learned (via auto-encoder) representation of the atom types with an inner product space on atoms based on scientific knowledge (e.g., electronegativity). We will illustrate how this approach captures key chemical properties of the molecules and compare the energy calculations with state-of-the-art neural network approaches. However, to compute the resulting Laplacian involves a mixture of sparse and dense matrix computation and yields a dense matrix as the basis for the graph convolution. This dense convolutional kernel necessitates moving away from the standard message passing framework for graph neural networks and increases the computational cost of applying the kernel. In order to mitigate these costs we investigate means of leveraging the mixed sparse and dense computations to reduce the overall computational cost and how these approaches can be automatically transferred to energy efficient hardware (e.g., field programmable gate arrays (FPGAs)).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-time Object Bounding in LiDAR Data With Computer Vision

The Multimodal Measurement System is a roadside radiation measurement testbed used to detect radiation sources in passing vehicles. It works by combining sensor signals from various modalities to produce a thorough scan of the source. A LiDAR sensor is used to measure the dimensions of the vehicle and provide a velocity estimate. However, the current LiDAR setup uses propriety software for which the source code is unavailable and cannot be updated to improve performance. Therefore, it is imperative to the accuracy of the analysis to create a custom vehicle detection that can return the dimensions and velocity of passing vehicles in real time. This new custom detection is written in C++ using the PointCloud Library, which keeps it lightweight. It also utilizes Docker and the Robot Operating System, which allows the versatility of running both on a small computer or the Lawrence Livermore National Laboratory cluster while utilizing different models of LiDAR sensors. The custom detection outperforms the current detection model, which increases the accuracy of radiation source detection.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Electronic excitation spectra of molecular hydrogen in phase I from quantum Monte Carlo and many-body perturbation methods

Here, we study the electronic excitation spectra in solid molecular hydrogen (phase I) at ambient temperature and 5- to 90-GPa pressures using quantum Monte Carlo methods and many-body perturbation theory. In this range, the system changes from a wide-gap molecular insulator to a semiconductor, altering the nature of the excitations from localized to delocalized. Computed gaps and spectra agree with experiments, proving the ability to predict accurately band gaps of many-body systems in the presence of nuclear quantum and thermal effects.

08 HYDROGEN↗
DOE OSTI2024

Enabling Capabilities and Resources: 2024 Principal Investigator Meeting Proceedings

As a major supporter of basic genome-enabled research, BER’s Biological Systems Science Division (BSSD) fosters scientific discovery by funding - fundamental biological research across disciplines in conjunction with enabling investigational tools and computational capabilities that include world-class user facilities. The overarching goal of BSSD is to provide the necessary fundamental science to understand, predict, manipulate, and design biological systems that underpin innovations for bioenergy and bioproduct production and enhance understanding of natural, DOE-relevant environmental processes (Biological Systems Science Division Strategic Plan, 2021). To accelerate the U.S. bioeconomy, BSSD pursues innovative science underpinning advances in sustainable biofuels and bioproducts and the development of next-generation technologies and computational resources for systems biology research. The 2024 BSSD Enabling Capabilities and Resources (ECR) Principal Investigator (PI) meeting brought together PIs across the BSSD ECR portfolio to confer on shared interests and opportunities. The meeting was held concurrently with the Genomic Science program (GSP) PI meeting to optimize collaboration on research to advance bioenergy and the bioeconomy. Rick Stevens of Argonne National Laboratory gave a keynote on How Generative Artificial Intelligence Can Impact Biological Research (see Keynote: How Generative Artificial Intelligence Can Impact Biological Research, this page). Plenary presentations included several joint sessions that illuminated the integration and understanding of the larger BSSD mission. GSP’s objective is to provide systems-level understanding of plants, microbes, and their communities through its Bioenergy Research, Biosystems Design, and Environmental Microbiome Research portfolios. The objective of the ECR portfolio is to support development of computational and instrumental platforms to advance fundamental GSP research—and BER more broadly— toward the overall goal of understanding the functional principles of living systems and their response to environmental challenges.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Multimodal Approaches for Leveraging Domain Knowledge with State-of-the-Art Machine Learning to Engineer Biocatalysts

This grant aimed to accelerate the development of specialized enzymes—biological catalysts essential for sustainable manufacturing and medicine—by integrating traditional laboratory evolution with cutting-edge artificial intelligence. To achieve this, we developed a suite of high-throughput sequencing tools and a centralized database to bridge the gap between a protein’s genetic "code" and its physical function. By training machine learning models on large datasets, we also demonstrated the ability to move beyond slow, trial-and-error testing to a "generative" approach, where AI can independently design new, versatile enzymes like tryptophan synthases. Ultimately, these findings demonstrate that combining laboratory data with computer-guided design enables the engineering of highly efficient biological tools with unprecedented speed and precision.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Multi-level, forming and filament free, bulk switching trilayer RRAM for neuromorphic computing at the edge

CMOS-RRAM integration holds great promise for low energy and high throughput neuromorphic computing. However, most RRAM technologies relying on filamentary switching suffer from variations and noise, leading to computational accuracy loss, increased energy consumption, and overhead by expensive program and verify schemes. We developed a filament-free, bulk switching RRAM technology to address these challenges. We systematically engineered a trilayer metal-oxide stack and investigated the switching characteristics of RRAM with varying thicknesses and oxygen vacancy distributions to achieve reliable bulk switching without any filament formation. We demonstrated bulk switching at megaohm regime with high current nonlinearity, up to 100 levels without compliance current. We developed a neuromorphic compute-in-memory platform and showcased edge computing by implementing a spiking neural network for an autonomous navigation/racing task. Our work addresses challenges posed by existing RRAM technologies and paves the way for neuromorphic computing at the edge under strict size, weight, and power constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Robust wind farm layout optimization

Wake interactions in wind farms cause losses in annual energy production (AEP) on the order of 10%. Wind farm designers optimize the layout of the farm to mitigate wake losses, especially in the dominant site-specific wind directions. As wind turbines and wind farms grow in scale, optimization becomes more complex. Offshore wind farms regularly comprise more than 100 wind turbines and are characterized by complex boundaries due to shipping lanes, neighboring wind farms, and other constraints. Layout optimization methods are broadly split between gradient-based and gradient-free approaches. Gradient-based approaches can converge quickly and perform well for smaller, academic problems but are often sensitive to initial conditions and tuning parameters and require expert knowledge to use. On the other hand, gradient-free approaches can be more robust to problem complexities. We present a robust layout optimization approach based on a random search algorithm. The algorithm is intended for those who are not optimization experts and has few tuning parameters that need specification to achieve satisfactory results. Unlike off-the-shelf methods, which use generally available, non-domain-specific optimization routines that accept as inputs an optimization function and constraint definitions, this approach takes advantage of the relative computational costs of the different evaluations by evaluating cheaper computations first (boundary and minimum distance constraints) and running expensive AEP evaluations only if all other checks pass. Moreover, an outer genetic algorithm allows multiple solutions to evolve in parallel, enabling rapid solution development on high-performance computers. We discuss the relative ease of selecting necessary tuning parameters and demonstrate the efficacy of the genetic random search on a complex layout problem consisting of placing 70 turbines in a nonconvex and unconnected boundary region.

17 WIND ENERGY↗
DOE OSTI2025

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗