Search NASA⌕ Search

SEARCH · Search NASA

Results for “mathematical foundation”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Dakota A Multilevel Parallel Object-Oriented Framework for Design Optimization Parameter Estimation Uncertainty Quantification and Sensitivity Analysis (V.6.14) (Theory Manual)

The Dakota toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. Dakota contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic expansion methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the Dakota toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a theoretical manual for selected algorithms implemented within the Dakota software. It is not intended as a comprehensive theoretical treatment, since a number of existing texts cover general optimization theory, statistical analysis, and other introductory topics. Rather, this manual is intended to summarize a set of Dakota-related research publications in the areas of surrogate-based optimization, uncertainty quantification, and optimization under uncertainty that provide the foundation for many of Dakota's iterative analysis capabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Uncertainty Quantification for Component Modeling Using the Discrete-Direct Approach

Threaded fastener behavior can be an important aspect of complex component and system behavior, but there is no one-size-fits-all finite element analysis technique. Proper modeling of threaded fastener joints requires careful consideration of many details, from test setup and data acquisition to constitutive modeling and uncertainty quantification approaches. This report details analysis of a “mini-radax” bolted-joint exemplar where a Discrete-Direct uncertainty quantification approach is employed to evaluate margin of the component. The mini-radax geometry is tested to failure on a drop table, and single-coupon tests of individual fasteners serve as foundational data for the analysis. Analysis predictions complement the test data well and provide additional context for engineering decision-making.

42 ENGINEERING↗
DOE OSTI2024

Convergent Concordant Mode Approach for Molecular Vibrations: CMA-2

The concordant mode approach (CMA) is a promising new scheme for dramatically increasing the system size and level of theory achievable in quantum chemical computations of molecular vibrational frequencies. Here, we achieve advances in the CMA hierarchy by computations targeting CCSD(T)/cc-pVTZ (coupled cluster singles and doubles with perturbative triples using a correlation-consistent polarized-valence triple-ζ basis set) benchmarks within the G2 molecular test set, executing a statistical analysis for 1501 frequencies from 111 compounds and then separately solving the refractory case of pyridine. First, MP2/cc-pVTZ (second-order Møller–Plesset perturbation theory with the same basis set) proves to be an excellent and preferred choice for generating the underlying (Level B) normal modes of the CMA scheme. Utilizing this Level B within the CMA-0A method reproduces the 1501 benchmark frequencies with a mean absolute error (MAE) of only 0.11 cm –1 and an attendant standard deviation of 0.49 cm –1 . Second, a convergent CMA-2 method is constituted that allows efficient computation of higher level (Level A) frequencies to any reasonable accuracy threshold by using only Hartree–Fock (HF) and MP2 or density functional theory (DFT) data to generate ξ parameters, which select the sparse off-diagonal force field elements for explicit evaluation at Level A. When Level B = MP2/cc-pVTZ, a cutoff of ξ = 0.02 provides an average maximum absolute error per molecule of only 0.17 cm –1 by incurring merely a 33% increase in average cost over CMA-0A. This CMA-2 method also eradicates the 4 problematic CMA-0A outliers of pyridine with even less effort (ξ = 0.04, 22% increase). Finally, the newly developed CMA procedures are shown to be highly successful when applied to 1-(1H-pyrrol-3-yl)ethanol, a new test molecule with diverse types of vibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

CUDO: closed-form universal dwell-time optimization for computer-controlled optical surfacing

Precision optical figuring demands fast and accurate dwell time optimization to reach nanometer- and sub-nanometer-level accuracy in next-generation optical systems. We introduce CUDO (closed-form universal dwell-time optimization), the first, to the best of our knowledge, unified closed-form analytical framework that supports both function-form and matrix-form dwell time models in computer-controlled optical surfacing (CCOS). In contrast to traditional methods, which rely on iterative optimization and hyperparameter tuning, our framework derives direct analytical solutions with no adjustable parameters. This approach unifies the solution principles of existing methods within a single mathematical model, delivering three key advantages: (1) accuracy on par with, or superior to, iterative solvers, (2) substantial reduction in computation time, and (3) numerical robustness. Comparative studies with prior art confirm that closed-form solutions achieve equivalent residual error while removing runtime bottlenecks. By simplifying the implementation and enabling real-time, scalable deployment, CUDO establishes a practical foundation for future deterministic fabrication of large-aperture and high-performance optics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

COVID-19, An Exercise in Data Governance at Sandia National Laboratories

In April of 2020, Sandia National Laboratories had an urgent need to identify and manage the data that could be used to create mobile applications, models, reports, and visualizations to assist management in safely bringing the workforce onsite during the COVID-19 pandemic. Multiple divisions volunteered to design and build software solutions; meanwhile, requests for new data sources, including duplicate requests, were inundating Information Technology (IT) and data owners. The Enterprise Data Governance Team was assigned to resolve obtaining and accessing new sources of data in an accelerated timeframe. Through successful collaboration with multiple stakeholders and domain owners across Sandia, the Enterprise Data Governance Team rapidly developed a centralized data strategy and solution for use in safeguarding the Sandia workforce during the COVID-19 pandemic. This foundation enabled teams to successfully develop solutions, including reports for executives and management as well as the data for modeling and scientific analysis.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2026

From Ensemble Climate to Ensemble Impacts

Many climate-risk tools rely on ensemble mean projections or endpoint climate snapshots to characterize future hazards. Although convenient for communication, these representations remove the statistical, temporal, and physical information that real infrastructure systems respond to. Infrastructure degradation and failure arise from extremes, sequences, cumulative stress, compound hazards, and nonlinear fragility relationships, none of which survive ensemble averaging or temporal compression. Power-system failure statistics and cascading failure models further show that infrastructure risk is dominated by tail events and path-dependent dynamics rather than by mean conditions. This paper demonstrates why ensemble mean or endpoint-only climate representations are mathematically and physically inconsistent with engineering-grade risk analysis. We outline a model-resolved, time-series-based workflow that preserves extremes, variability, and sequencing by propagating each climate-model realization independently through hazard formation, exposure, fragility, and cascading failure mechanisms. Taking the ensemble of impacts—rather than the ensemble of climate—provides a defensible, physically coherent foundation for infrastructure resilience planning, regulatory compliance, and long-term investment decisions.

54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗
DOE OSTI2024

The Essence of Cryptol: A Denotational Cryptol Interpreter in Coq for Foundational Assurances for Quantum Resistant Cryptosystems

Systems of the utmost consequence need a means to establish authenticity of software and data. Cryptosystems implement authentication, but can be vulnerable to cryptographic and implementation attacks. With the threat of quantum cryptographic attacks, “post-quantum” cryptosystems (PQCs) must be henceforth used in these systems. However, the new cryptography needs new ways to, rigorously and machine-checkably, prove systems free of vulnerabilities. We propose a retargetable capability to rapidly instantiate proven correct postquantum cryptosystems through novel proof-carrying synthesis and proof-automation technique, extending those proven successful on existing systems. This capability is crucial to meeting the cryptographic requirements for future high-consequence systems. Since specifications for high consequence cryptography are presently captured in a domain specific language known as Cryptol. While this can enable convenient fully automated reasoning about Cryptol specificaitons and implementations via the Software Analysis Workbench (SAW), Cryptol has expressivity gaps, so that cryptosystems with probabilistic programming features like Falcon cannot be fully expressed in the language. Moreover, SAW’s automation fails for programs and specificaitons with inductive and recursive structure, as in the Sphincs+ PQC. Finally, Cryptol and SAW together represent some 200,000 lines of unverified Haskell, so that the any guarantees about high consequence cryptography are presently contingent on a large, unverified, yet trusted computing base. The first step of the larger project of agile, assured crpytography is therefore to provide a formal, mechanized semantics for Cryptol, so that the specifications expressed by cryptographers in Cryptol can be reasoned about and compiled into performant implementations with a foundational, machine checkable certificate of correctness. This report describes our work on this first step, culminating in the design of a certified denotational interpreter, in Coq, for core Cryptol.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

U.S. Hydropower Workforce: Challenges and Opportunities

Over the past four years, the National Renewable Energy Laboratory (NREL) has engaged with the hydropower industry, academia, and students to understand the perspectives and challenges of the U.S. hydropower workforce. This engagement and research were sponsored by the U.S. Department of Energy's (DOE's) Water Power Technologies Office as part of an NREL-led project—Water Power Science, Technology, Engineering, and Mathematics (STEM) to Workforce—which has the goal of developing tools and programs to strengthen the water power workforce pipeline. This report shares findings from that research and provides an update on U.S. hydropower workforce trends as a follow-on to NREL's 2019 report, Workforce Development for U.S. Hydropower: Key Trends and Findings (Keyser and Tegen 2019). Recent data from NREL, the Hydropower Foundation's survey efforts, and the hydropower industry are presented.

13 HYDRO ENERGY↗
DOE OSTI2026

plexosdb: A Modular Library for Programmatic PLEXOS Model Construction

plexosdb is a lightweight Python library for constructing PLEXOS models using a SQLite-backed data structure. It provides a clear, modular interface that maps relational data directly to model components. By leveraging SQLite and idiomatic Python, it enables fast iteration and reproducible workflows. The result is a performant, composable foundation for scalable PLEXOS model development.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Understanding the Interplay between the Nonvalence and Valence States of the Uracil Anion upon Monohydration

In this work we present an ab initio investigation into the effect of monohydration on the interaction of uracil with low energy electrons. Electron attachment and photodetachment experimental studies have previously shown dramatic changes in uracil upon solvation with even a single water molecule, due to an inversion of the character of the ground state of the anion. Here we explore the interplay between the nonvalence and valence states of the uracil anion, as a function of geometry and site of solvation. Our model provides unambiguous interpretation of previous photoelectron studies, reproducing the binding energies and photoelectron images for bare uracil and a single isomer of the U•(H 2 O) 1 cluster. Furthermore, the results of this study provide insight into how electrons may attach to hydrated nucleobases. These results lay the foundations for further investigations into the effect of microhydration on the electronic structure and electron capture dynamics of nucleobases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Linking metabolic phenotypes to pathogenic traits among “ Candidatus Liberibacter asiaticus” and its hosts

Candidatus Liberibacter asiaticus (CLas) has been associated with Huanglongbing, a lethal vector-borne disease affecting citrus crops worldwide. While comparative genomics has provided preliminary insights into the metabolic capabilities of this uncultured microorganism, a comprehensive functional characterization is currently lacking. Here, we reconstructed and manually curated genome-scale metabolic models for the six CLas strains A4, FL17, gxpsy, Ishi-1, psy62, and YCPsy, in addition to a model of the closest related culturable microorganism, L. crescens BT-1. Predictions about nutrient requirements and changes in growth phenotypes of CLas were confirmed using in vitro hairy root-based assays, while the L. crescens BT-1 model was validated using cultivation assays. Host-dependent metabolic phenotypes were revealed using expression data obtained from CLas-infected citrus trees and from the CLas-harboring psyllid Diaphorina citri Kuwayama. These results identified conserved and unique metabolic traits, as well as strain-specific interactions between CLas and its hosts, laying the foundation for the development of model-driven Huanglongbing management strategies.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Efficient online quantum circuit learning with no upfront training

Optimization is a promising candidate for studying the utility of variational quantum algorithms (VQAs). However, evaluating cost functions using quantum hardware introduces runtime overheads that limit exploration. Surrogate-based methods can reduce calls to a quantum computer, yet existing approaches require hyperparameter pre-training and have been tested only on small problems. Here, we show that surrogate-based methods can enable successful optimization at scale, without pre-training, by using radial basis function interpolation (RBF) to construct an adaptive, hyperparameter-free surrogate. Using the surrogate as an acquisition function drives hardware queries to the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut instances with the Quantum Approximate Optimization Algorithm (QAOA), our method outperforms state-of-the-art approaches, without considering their upfront training costs. Furthermore, we successfully optimize QAOA circuits for 127-qubit random Ising models on an IBM processor using 10 4 −10 5 measurements. Strong empirical performance demonstrates the promise of automated surrogate-based learning for large-scale VQA applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

ORBIT-2 Dataset for Scaling Exascale Vision Foundation Models for Weather and Climate Downscaling

This dataset release corresponds to the work conducted in ORBIT-2: Scaling Exascale Vision Foundation Models for Weather and Climate Downscaling, where large-scale AI methods were applied to improve climate and weather resolution. The collection integrates four widely used, publicly available datasets: ERA5, PRISM, DAYMET, and IMERG. To prepare the data for ORBIT-2 model training and evaluation, we applied a preprocessing pipeline that generates paired low-resolution and high-resolution samples, enabling supervised downscaling experiments. The transformation from coarse to fine scales was performed using bilinear regridding, consistent with the procedures described in WeatherBench2, a community benchmark for weather and climate AI models. This dataset supports the development and evaluation of foundation models designed for weather and climate downscaling at exascale. Additional details on methodology and applications can be found in Wang et al., ORBIT-2 (arXiv:2505.04802, 2025).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

CMakePPLang: An object-oriented extension to CMake

CMakePPLang is an object-oriented extension to the CMake language written entirely using the original CMake language, with the goal of making projects built on CMake easier to create and maintain. That said, CMakePPLang has different coding practices, paradigms, and standards than the original CMake language, much in the same way that C++ coding differs from C coding despite some level of interoperability. Currently, CMakePPLang is used within the CMakePP organization as the foundation for two in-progress projects: CMakeTest and CMaize. CMakeTest provides a solution for unit testing CMake and CMakePPLang code. CMaize is a CMake tool to simplify interoperability between projects and writing their build systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Neural operator transformers capture bifurcating drift-wave turbulence in fusion plasma simulations

Self-consistent modeling of turbulence-driven transport is critical for optimizing confinement in magnetically confined fusion plasmas, such as tokamaks and stellarators. In particular, capturing the long-term co-evolution of turbulence, flow, and background plasma profiles remains computationally challenging. Direct numerical simulation of these multiscale, highly nonlinear processes is often demanding and impractical for real-time control or design optimization. To address this bottleneck, we investigate transformer-based neural operator partial differential equation surrogates for emulating the dynamics of drift-wave turbulence bifurcation mediated by zonal flows, using the modified Hasegawa–Wakatani (MHW) model as a prototypical system. We find that the finetuned neural operator model has excellent performance in capturing the multi-spatiotemporal-scales of MHW turbulence bifurcation and is robust to testing on rare and out-of-distribution dynamics. Specifically, we demonstrate that a single unified model accurately predicts both quasi-steady-state turbulence and a wide range of dynamical transition processes, such as nonlinear saturation, spontaneous suppression of turbulence, and the emergence of macroscopic zonal flows, over time horizons vastly exceeding the local turbulence correlation time. This computationally efficient approach establishes a strong foundation for fast, AI-based modeling of complex, multiscale phenomena in magnetized fusion plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Development and Validation of Physics-Based Sub-Models of High-Pressure Supercritical Fuel Injection at Diesel Conditions Insert

The project sought to develop and validate accurate, physics-based, numerical submodels and implement them in computational fluid dynamics (CFD) software codes to enable accurate predictions of diesel sprays at pressures higher than the current systems. The combined experimental-computational effort has four main objectives: (1) acquire spatially and temporally resolved scalar measurements of fuel-oxidizer mixing in the near field of the fuel jet, (2) develop software modules to calculate thermo-physical properties of diesel surrogates and their mixtures with oxidizer of interest in real-gas operating regime, (3) integrate the real-fluid model into a commercial and an open-source CFD code to simulate fuel-air mixing in high-pressure diesel sprays, and (4) assess the robustness, accuracy, and uncertainty of the integrated CFD solvers in computing diesel sprays. Project accomplishments are consistent with the original goals of the project. Although we acquired spatially and temporally resolved scalar measurements, they were limited to refractive index difference and not to thermodynamic properties such as temperature and equivalence ratio. However, we successfully developed the theoretical background needed to acquire such measurements at diesel conditions and demonstrated the capability of the RSD for scalar measurements in a canonical turbulent jet flow replicating features of the diesel jet. Additional work will be needed to implement these procedures at high-pressure, high-temperature engine-like conditions of the CPFR. Mainly, we did not anticipate the need to find the liquid boundary and its statistical features or the state relationships between refractive index and thermodynamic properties, assuming the widely known Dale-Gladstone equation would suffice. Still, efforts devoted to these tasks were essential to fulfil the goals of the project and serves as the foundation on which many of the conclusions and key contributions of this project are based. Further assessment and application of the developed CFD codes is recommended to fully realize the benefits of this research.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

2022 American Conference on Neutron Scattering (ACNS 2022)

The 11th American Conference on Neutron Scattering (ACNS 2022) will be held on June 5-9, 2022, in Boulder, CO. The Conference will provide essential information on the breadth and depth of current neutron-related research worldwide. Hosted by the Neutron Scattering Society of America, this year’s Conference will feature a combination of invited and contributed talks, poster sessions, and tutorials. Topics of the conference are: Advances in Neutron Facilities, Instrumentation and Software: Developments in sources, instrumentation, sample environments and control software. Hard Condensed Matter: Magnetism, correlated metals, quantum/topological materials, superconductors, ferroelectrics, multiferroics, glasses, and disorder phenomena. Submissions outlining examples of neutron scattering in industrial and engineering applications involving hard condensed matter systems are also encouraged. Soft Matter: Neutron studies of soft materials and related fields including in situ and in operando studies. Polymers, surfactants, emulsions, gels, nanoparticles, colloidal suspensions and more. Submissions of computational studies or applications of machine learning beneficial to neutron scattering experiments, as well as examples of neutron scattering in industrial and engineering applications are strongly encouraged. Biology, Biophysics and Biotechnology: Neutron studies of biological and biologically relevant systems. Proteins, bio membranes, biological assemblies, natural materials, nucleic acids, drug-delivery platforms and biomedical systems. Submissions of computational studies or applications of machine learning beneficial to biological neutron scattering experiments, as well as examples of neutron scattering in applied research involving biological systems, are strongly encouraged. Materials Chemistry and Energy: Neutron-based studies of functional materials and materials for energy applications. Examples include porous materials such as metal organic frameworks (MOFs), zeolites; phosphors; novel pigments; electrolytes; catalysts; ionic conductors/cathode materials; photovoltaic materials (hybrid perovskites); thermoelectrics; magnetocalorics/electrocalorics. Structural Materials and Engineering: Neutron scattering studies of materials and engineering processes including structural materials, concrete and metals, as well as engineering processes including combustion, corrosion, additive manufacturing, and others. Neutron Physics: Fundamental physical studies of the neutron and related areas. Emerging Applications in Neutron Scattering: Machine Learning and Data Science: Advances in computing power have contributed to rapidly evolving machine learning and data science fields that can be leveraged to the benefit of the neutron scattering community. The purpose of this session is to highlight recent advances in machine learning and data science and to serve as the foundation of a parallel data and computation track highlighting computation advances and applications in neutron scattering throughout the conference.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bayesian Optimization for Reactor Design Optimization

This study present a test case in which the Bayesian Optimization method is applied to a simulation-based reactor core design optimization problem. The test case aims to showcase the potential of an automated design optimization algorithm for reactor designs by streamlining the reactor core design workflow, given the high computational cost of simulations. The contributions of this work are threefold. First, the existing HTGR model is converted into a simulation-based design optimization test case by developing a pipeline that enables modification of key design parameters and evaluates design performance based on simulation outputs. Second, Bayesian Optimization is implemented and adapted to demonstrate the feasibility of automatic design optimization for nuclear reactor core. Proposed approach leverages Gaussian Process models to characterize the relationship between design variables and performance metrics, while incorporating novel acquisition functions that balance exploration of the design space with exploitation of promising configurations. This implementation lays the foundation for the future developments of reactor design optimization algorithms.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗