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Results for “Mathematical optimization”

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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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Affine Transformations to Enable Machine Learning for Semi-Quantitative EDS Analysis

Energy Dispersive X-ray Spectroscopy (EDS) is an essential technique for determining elemental concentrations and distributions within microstructures, critical for materials discovery, optimization, and qualification. However, most published EDS data is qualitative because current quantitative EDS analysis methods require extensive calibration and post-processing, limiting their practicality and widespread adoption. This work seeks to establish a framework for accelerated EDS characterization and spectrum analysis that can leverage ML to analyze correlations between various elemental compositions and resulting EDS spectra. The complex physics and data result in a high-dimensional problem that grows exponentially with the number of elements in the system and the complexity of the spectrum analysis. ML provides a way to compute and optimize the results of this highly dimensional problem in a flexible way to tailor it to the user’s specific needs and material system. However, the framework emphasizes transparency through a strictly mathematical affine transformation, so the analysis remains understandable and reviewable to facilitate adoption by the scientific community. While currently implemented methods are simplistic and unvalidated, further development and demonstration of this framework could enable high-throughput, accurate, and accessible EDS characterization.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2026

Affine Transformations to Correlate Experimental and Simulated EDS Spectra for Multi-Element Systems

Energy Dispersive X-ray Spectroscopy (EDS) is an essential technique for determining elemental concentrations and distributions within microstructures, critical for materials discovery, optimization, and qualification. However, most published EDS data is qualitative because current quantitative EDS analysis methods require extensive calibration and post-processing, limiting their practicality and widespread adoption. This work seeks to establish a framework for accelerated EDS characterization and spectrum analysis that can leverage ML to analyze correlations between various elemental compositions and resulting EDS spectra. The complex physics and data result in a high-dimensional problem that grows exponentially with the number of elements in the system and the complexity of the spectrum analysis. ML provides a way to compute and optimize the results of this highly dimensional problem in a flexible way to tailor it to the user’s specific needs and material system. However, the framework emphasizes transparency through a strictly mathematical affine transformation, so the analysis remains understandable and reviewable to facilitate adoption by the scientific community. While currently implemented methods are simplistic and unvalidated, further development and demonstration of this framework could enable high-throughput, accurate, and accessible EDS characterization.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1986

Optimization of the geometric dimensions of vertical electrolyzers with gas-generating electrodes

A study is made to determine whether, under the conditions of electrolyte circulation induced by evolved gases, it is possible to increase the vertical scale without a great increase in cell voltage. The mathematical modeling used is discussed, and a comparison is made with experimental results and conclusions. It is found that it is possible to increase the vertical scale without producing a cell voltage increase.

Thiele, W.↗
DOE OSTI2026

Multibody for Everybody (M4E): A Symbolic Dynamics Modeling Tool with Applications in Simulation, Control, and Optimization

Developing the analytical model of a multibody system is often the initial step in control and optimization. The analytical model (equations of motion) describes a system’s time evolution under specified forcing conditions. Although developing these equations is easy for simple systems, this process becomes more complex for systems composed of multiple bodies. Deriving equations of motion for complex multibody systems requires specialized expertise in multibody dynamics, is time-consuming, and is susceptible to error. To address this issue, this paper presents an open-source, easy-to-use, systematic framework to derive symbolic equations of motion in both Python and MATLAB using the joint coordinate formulation. This formulation results in a set of ordinary differential equations that use the minimum set of coordinates needed to model a system. The symbolic representation provides better insight into the influence of design parameters on system performance, facilitates sensitivity analysis and parameter studies, and supports direct implementation of control and optimization routines. The tool enables numerical simulation for specified parameter sets, is modular for straightforward integration with other tools and libraries, and allows incorporation of hydrodynamics, mooring, and other external forces. The result is a reproducible, extensible pipeline for modeling, simulation, and design of complex multibody systems. The proposed tool is versatile and can be applied to domains such as robotics, control, and design. In addition, we integrated external libraries that provide capabilities for modeling offshore systems such as underwater robots and marine energy converters.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Unconventional Quantum Advantages for Computation (U-QuAC)

While quantum computing offers the promise of exponential advantages, limited quantum speedups are known, especially for practical applications. To open new avenues for quantum advantages, we propose Unconventional Quantum Advantages for Computation (U-QuACs), with respect to unconventional resources such as space (number of bits or quantum bits of memory required to solve a problem), accuracy of solution, communication, or energy consumption. We focus on space-efficient quantum algorithms, where we seek to design algorithms that solve a problem using much less space than the total size of the input. A natural setting in which space is critical is the streaming model of computation, where the input data arrives sequentially in pieces that must each be processed individually. Streaming is motivated by a variety of problems including analysis of internet traffic or social networks. We design the first exponential quantum space advantage for a natural streaming problem, which also constitutes the first quantum advantage for approximating a discrete optimization problem, albeit with respect to space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Advanced Data Center Energy Opportunities: Cloud and Infrastructure CoP - Data Center Energy and Efficiency with AI Adoption

The NLR portion of the "Cloud & Infrastructure CoP - Data Center Energy and Efficiency with AI Adoption" web meeting will cover data center locations, energy use and load growth, best practices, performance metrics, transition to direct liquid cooled data center equipment, and NLR's approach to optimizing data center.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS1972

A comparison of optimal and noise-abatement trajectories of a tilt-rotor aircraft

The potential benefits of flight path control to optimize performance and/or reduce the noise of a tilt-rotor aircraft operating in the takeoff and landing phases of flight are investigated. A theoretical performance-acoustic model is developed and then mathematically flown to yield representative takeoff and landing profiles. Minimum-time and minimum-fuel trajectories are compared to proposed noise-abatement profiles to assess the reductions in annoyance possible through flight path control. Significant reductions are feasible if a nearly vertical-takeoff flight profile is flown near the landing site; however, the time expended and fuel consumed increase.

Schmitz, F. H.↗
NASA NTRS1984

Dynamics and control of flexible orbiting systems

Mathematical modeling and design analysis is carried out for large flexible spacecraft and antenna systems. Modeling topics include inertially fixed attitude stabilization, solar radiation pressure effects, control systems for space mast structures, and optimal control of a hoop/column space antenna system. Each subject includes a brief overview of the pertinent literature and details of the proposed solutions for the specific modeling tasks.

Bainum, P. M.↗
NASA NTRS1993

A numerical approach to controller design for the ACES facility

In recent years the employment of active control techniques for improving the performance of systems involving highly flexible structures has become a topic of considerable research interest. Most of these systems are quite complicated, using multiple actuators and sensors, and possessing high order models. The majority of analytical controller synthesis procedures capable of handling multivariable systems in a systematic way require considerable insight into the underlying mathematical theory to achieve a successful design. This insight is needed in selecting the proper weighting matrices or weighting functions to cast what is naturally a multiple constraint satisfaction problem into an unconstrained optimization problem. Although designers possessing considerable experience with these techniques have a feel for the proper choice of weights, others may spend a significant amount of time attempting to find an acceptable solution. Another disadvantage of such procedures is that the resulting controller has an order greater than or equal to that of the model used for the design. Of course, the order of these controllers can often be reduced, but again this requires a good understanding of the theory involved.

Frazier, W. Garth↗
NASA NTRS2004

Human-Interaction Challenges in UAV-Based Autonomous Surveillance

Autonomous UAVs provide a platform for intelligent surveillance in application domains ranging from security and military operations to scientific information gathering and land management. Surveillance tasks are often long duration, requiring that any approach be adaptive to changes in the environment or user needs. We describe a decision- theoretic model of surveillance, appropriate for use on our autonomous helicopter, that provides a basis for optimizing the value of information returned by the UAV. From this approach arise a range of challenges in making this framework practical for use by human operators lacking specialized knowledge of autonomy and mathematics. This paper describes our platform and approach, then describes human-interaction challenges arising from this approach that we have identified and begun to address.

Freed, Michael↗
NASA NTRS1996

Considerations in miniaturizing simplified agro-ecosystems for advanced life support

Miniaturizing the Earth's biogeochemical cycles to support human life during future space missions is the goal of the NASA research and engineering program in advanced life support. Mission requirements to reduce mass, volume, and power have focused efforts on (1) a maximally simplified agro-ecosystem of humans, food crops, and microbes; and, (2) a design for optimized productivity of food crops with high light levels over long days, with hydroponics, with elevated carbon dioxide and other controlled environmental factors, as well as with genetic selection for desirable crop properties. Mathematical modeling contributes to the goals by establishing trade-offs, by analyzing the growth and development of experimental crops, and by pointing to the possibilities of directed phasic control using modified field crop models to increase the harvest index.

Non-NASA Center↗
DOE OSTI2024

Leveraging Optimal Sparse Sensor Placement to Aggregate a Network of Digital Twins for Nuclear Subsystems

Nuclear power plants (NPPs) require continuous monitoring of various systems, structures, and components to ensure safe and efficient operations. The critical safety testing of new fuel compositions and the analysis of the effects of power transients on core temperatures can be achieved through modeling and simulations. They capture the dynamics of the physical phenomenon associated with failure modes and facilitate the creation of digital twins (DTs). Accurate reconstruction of fields of interest (e.g., temperature, pressure, velocity) from sensor measurements is crucial to establish a two-way communication between physical experiments and models. Sensor placement is highly constrained in most nuclear subsystems due to challenging operating conditions and inherent spatial limitations. This study develops optimized data-driven sensor placements for full-field reconstruction within reactor and steam generator subsystems of NPPs. Optimized constrained sensors reconstruct field of interest within a tri-structural isotropic (TRISO) fuel irradiation experiment, a lumped parameter model of a nuclear fuel test rod and a steam generator. The optimization procedure leverages reduced-order models of flow physics to provide a highly accurate full-field reconstruction of responses of interest, noise-induced uncertainty quantification and physically feasible sensor locations. Accurate sensor-based reconstructions establish a foundation for the digital twinning of subsystems, culminating in a comprehensive DT aggregate of an NPP.

42 ENGINEERING↗
DOE OSTI2026

Semi-Analytical Hierarchical Bayesian Inference of Nonlinear Model Structure in Stochastic Dynamics: Applied to Compartmental Models of Infectious Diseases

A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Digital Twins for Data Centers

Fueled by an unprecedented adoption of AI (Artificial Intelligence), data centers are becoming the largest growing consumers of energy. Digital Twins provide living digital models of physical systems that enable data-driven analysis and application of AI to better manage selective aspects of the data center and drive efficiency for sustainability. Digital twins have emerged as a way to create virtual prototypes of physical artifacts, which may be used in a variety of contexts. Physical artifacts include airplanes, factories, or even static objects, such as bridges or dams. Digital twin helps monitor changes and assist in predicting planned or unplanned behaviors of physical objects. In this paper, we discuss digital twins for data centers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Segregation effects during solidification in weightless melts

Computer programs are developed and used in the study of the combined effects of evaporation and solidification in space processing. The temperature and solute concentration profiles during directional solidification of binary alloys with surface evaporation were mathematically formulated. Computer results are included along with an econotechnical model of crystal growth. This model allows: prediction of crystal size, quality, and cost; systematic selection of the best growth equipment or alloy system; optimization of growth or material parameters; and a maximization of zero-gravity effects. Segregation in GaAs crystals was examined along with vibration effects on GaAs crystal growth. It was found that a unique segregation pattern and strong convention currents exist in GaAs crystal growth. Some beneficial effects from vibration during GaAs growth were discovered. The implications of the results in space processing are indicated.

Li, C.↗