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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Isotopically nonstationary metabolic flux analysis of plants: recent progress and future opportunities

Metabolic flux analysis (MFA) is a valuable tool for quantifying cellular phenotypes and to guide plant metabolic engineering. By introducing stable isotopic tracers and employing mathematical models, MFA can quantify the rates of metabolic reactions through biochemical pathways. Recent applications of isotopically nonstationary MFA (INST–MFA) to plants have elucidated nonintuitive metabolism in leaves under optimal and stress conditions, described coupled fluxes for fast–growing algae, and produced a synergistic multi–organ flux map that is a first in MFA for any biological system. Finally, these insights could not be elucidated through other approaches and show the potential of INST–MFA to correct an oversimplified understanding of plant metabolism.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Complete Demonstration of a Prototype Version of FORCE User Interface and Conduct Analyst Survey Collecting Feedback on Interface Features and Usability

In 2024 the US Department of Energy (DOE) Office of Nuclear Energy (NE) Integrated Energy System (IES) program continued to develop the Framework for Optimization of Resources and Economics (FORCE) analysis ecosystem into a more traditional toolset with simplified software installation, automated workflows, and interactive results visualization. The DOE-NE Nuclear Energy Advanced Modeling and Simulation (NEAMS) Workbench continued to be leveraged for user input, application workflow and runtime environment, and interactive results visualization capabilities. This report documents the demonstration of a FORCE User Interface (UI) prototype and the results of a survey of analysts’ using the Holistic Energy Resource Optimization Network (HERON) tool in FORCE with the prototype UI.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Laminar flow effects in the coil planet centrifuge

The coil planet centrifuge designed by Ito employs flow of a single liquid phase, through a rotating coiled tube in a centrifugal force field, to provide a separation of particles based on sedimentation rates. Mathematical solutions are derived for the linear differential equations governing particle behavior in the coil planet centrifuge device. These solutions are then applied as the basis of a model for optimizing particle separations.

Herrmann, F. T.↗
DOE OSTI2025

Leveraging prior mean models for faster Bayesian optimization of particle accelerators

Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major advantages of Bayesian algorithms is the ability to incorporate prior information about beam physics and historical behavior into the model used to make control decisions. In this work, we examine incorporating prior accelerator physics information into Bayesian optimization algorithms by utilizing fast executing, neural network models trained on simulated or historical datasets as prior mean functions in Gaussian process models. We show that in ideal cases, this technique substantially increases convergence speed to optimal solutions in high-dimensional tuning parameter spaces. Additionally, we demonstrate that even in non-ideal cases, where prior models of beam dynamics do not exactly match experimental conditions, the use of this technique can still enhance convergence speed. Finally, we demonstrate how these methods can be used to improve optimization in practical applications, such as transferring information gained from beam dynamics simulations to online control of the LCLS injector, and transferring knowledge gained from experimental measurements across different operating modes, such as accelerating different ion species at the ATLAS heavy ion accelerator.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Generative AI in Supply Chain Management: Applications, Challenges, and Future Directions

Supply chain management (SCM) is undergoing rapid transformation due to increasing global complexity, demand volatility, and operational disruptions. Generative Artificial Intelligence (GenAI) has emerged as a powerful paradigm capable of synthesizing data, simulating operational scenarios, and enabling adaptive decision-making across supply chain networks. This paper presents a survey of GenAI’s role in SCM, focusing on its applications in predictive analytics, autonomous logistics, and fraud detection. Unlike traditional AI systems that rely primarily on predictive analytics, GenAI models, including large language models, generative adversarial networks, and diffusion-based architectures, enable the creation of synthetic supply chain scenarios and autonomous optimization strategies. This survey provides (1) a taxonomy of GenAI techniques for supply chain applications, (2) a comparative analysis of generative AI approaches with traditional machine learning, reinforcement learning, and blockchain-based methods, and (3) a discussion of key challenges such as data privacy, interpretability, and integration with legacy enterprise systems. Furthermore, we outline open research problems and propose directions for future research toward autonomous, resilient, and sustainable AI-driven supply chains.

15 - GEOTHERMAL ENERGY↗
NASA NTRS1979

Mathematical description and program documentation for CLASSY, an adaptive maximum likelihood clustering method

Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.

Lennington, R. K.↗
NASA NTRS1986

Czochralski growth of crystals - Simple models for growth rate and interface shape

A simple model for the crystal growth by the Czochralski (CZ) process has been proposed based on semiquantitative arguments. The model provides empirical relationships for the dependence of the pulling rate and the interface shape on the important process variables such as crystal radius, crucible temperature, height of the melt level, and the height of the exposed portion of the crucible wall. The parameters of the model can be evaluated by matching the results obtained from a detailed mathematical model of the CZ process or from extensive experimental data. The model has, therefore, the potential application for determining the best process conditions and for on-line control and optimization of the crystal puller to grow crystals with constant diameter and nearly planar interface.

Srivastava, R. K.↗
NASA NTRS1990

Parameter learning for performance adaptation

A parameter learning method is introduced and used to broaden the region of operability of the adaptive control system of a flexible space antenna. The learning system guides the selection of control parameters in a process leading to optimal system performance. A grid search procedure is used to estimate an initial set of parameter values. The optimization search procedure uses a variation of the Hooke and Jeeves multidimensional search algorithm. The method is applicable to any system where performance depends on a number of adjustable parameters. A mathematical model is not necessary, as the learning system can be used whenever the performance can be measured via simulation or experiment. The results of two experiments, the transient regulation and the command following experiment, are presented.

Peek, Mark D.↗
NASA NTRS1996

CometBoards Users Manual Release 1.0

Several nonlinear mathematical programming algorithms for structural design applications are available at present. These include the sequence of unconstrained minimizations technique, the method of feasible directions, and the sequential quadratic programming technique. The optimality criteria technique and the fully utilized design concept are two other structural design methods. A project was undertaken to bring all these design methods under a common computer environment so that a designer can select any one of these tools that may be suitable for his/her application. To facilitate selection of a design algorithm, to validate and check out the computer code, and to ascertain the relative merits of the design tools, modest finite element structural analysis programs based on the concept of stiffness and integrated force methods have been coupled to each design method. The code that contains both these design and analysis tools, by reading input information from analysis and design data files, can cast the design of a structure as a minimum-weight optimization problem. The code can then solve it with a user-specified optimization technique and a user-specified analysis method. This design code is called CometBoards, which is an acronym for Comparative Evaluation Test Bed of Optimization and Analysis Routines for the Design of Structures. This manual describes for the user a step-by-step procedure for setting up the input data files and executing CometBoards to solve a structural design problem. The manual includes the organization of CometBoards; instructions for preparing input data files; the procedure for submitting a problem; illustrative examples; and several demonstration problems. A set of 29 structural design problems have been solved by using all the optimization methods available in CometBoards. A summary of the optimum results obtained for these problems is appended to this users manual. CometBoards, at present, is available for Posix-based Cray and Convex computers, Iris and Sun workstations, and the VM/CMS system.

Guptill, James D.↗
DOE OSTI2024

Nonlinear elasticity with the Shifted Boundary Method

Here, we propose a new unfitted/immersed computational framework for nonlinear solid mechanics, which bypasses the complexities associated with the generation of CAD representations and subsequent body-fitted meshing. This approach allows to speed up the cycle of design and analysis in complex geometry and requires relatively simple computer graphics representations of the surface geometries to be simulated, such as the Standard Tessellation Language (STL format). Complex data structures and integration on cut elements are avoided by means of an approximate boundary representation and a modification (shifting) of the boundary conditions to maintain optimal accuracy. An extensive set of computational experiments in two and three dimensions is included.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1979

Mathematical model for preventive maintenance scheduling

A model is formulated to describe the effect of the time interval chosen for preventive maintenance upon the frequency of failure and frequency of total maintenance. Trade-offs between these two frequencies are determined by computation of an optimal interval in the case where the failure distribution is known. For unknown distributions, an adaptive statistical technique is developed that converges to an optimal preventive maintenance interval. A numerical illustration is given.

Lorden, G.↗
NASA NTRS1989

A design procedure for the handling qualities optimization of the X-29A aircraft

A design technique for handling qualities improvement was developed for the X-29A aircraft. As with any new aircraft, the X-29A control law designers were presented with a relatively high degree of uncertainty in their mathematical models. The presence of uncertainties, and the high level of static instability of the X-29A caused the control law designers to stress stability and robustness over handling qualities. During flight test, the mathematical models of the vehicle were validated or corrected to match the vehicle dynamic behavior. The updated models were then used to fine tune the control system to provide fighter-like handling characteristics. A design methodology was developed which works within the existing control system architecture to provide improved handling qualities and acceptable stability with a minimum of cost in both implementation as well as software verification and validation.

Bosworth, John T.↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Options for Meeting Data Center Demand in Virginia: Focus on GETs and Reconductoring [Slides]

Data center demand growth in Virginia will need to met with many options - GETs and/or reconductoring have the potential to be part of the solution suite in the short-term and medium-term. Almost all GETs and reconductoring technologies have more favorable economics than transmission wires investments considering relatively low levels of existing wide-scale deployment. Deployment of GETs and/or reconductoring is not a one size fits all - requires detailed analysis. The complementary nature of GETs and/or reconductoring impacts have the potential to be synergistic (more congestion relief, more transfer capability, more cost savings - when implemented together).

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1992

Uncertainty management by relaxation of conflicting constraints in production process scheduling

Mathematical-analytical methods as used in Operations Research approaches are often insufficient for scheduling problems. This is due to three reasons: the combinatorial complexity of the search space, conflicting objectives for production optimization, and the uncertainty in the production process. Knowledge-based techniques, especially approximate reasoning and constraint relaxation, are promising ways to overcome these problems. A case study from an industrial CIM environment, namely high-grade steel production, is presented to demonstrate how knowledge-based scheduling with the desired capabilities could work. By using fuzzy set theory, the applied knowledge representation technique covers the uncertainty inherent in the problem domain. Based on this knowledge representation, a classification of jobs according to their importance is defined which is then used for the straightforward generation of a schedule. A control strategy which comprises organizational, spatial, temporal, and chemical constraints is introduced. The strategy supports the dynamic relaxation of conflicting constraints in order to improve tentative schedules.

Dorn, Juergen↗
NASA NTRS1995

Towards a formal semantics for Ada 9X

The Ada 9X language precision team was formed during the revisions of Ada 83, with the goal of analyzing the proposed design, identifying problems, and suggesting improvements, through the use of mathematical models. This report defines a framework for formally describing Ada 9X, based on Kahn's 'natural semantics', and applies the framework to portions of the language. The proposals for exceptions and optimization freedoms are also analyzed, using a different technique.

Guaspari, David↗
NASA NTRS1996

Estimation of the longitudinal and lateral-directional aerodynamic parameters from flight data for the NASA F/A-18 HARV

This progress report presents the results of an investigation focused on parameter identification for the NASA F/A-18 HARV. This aircraft was used in the high alpha research program at the NASA Dryden Flight Research Center. In this study the longitudinal and lateral-directional stability derivatives are estimated from flight data using the Maximum Likelihood method coupled with a Newton-Raphson minimization technique. The objective is to estimate an aerodynamic model describing the aircraft dynamics over a range of angle of attack from 5 deg to 60 deg. The mathematical model is built using the traditional static and dynamic derivative buildup. Flight data used in this analysis were from a variety of maneuvers. The longitudinal maneuvers included large amplitude multiple doublets, optimal inputs, frequency sweeps, and pilot pitch stick inputs. The lateral-directional maneuvers consisted of large amplitude multiple doublets, optimal inputs and pilot stick and rudder inputs. The parameter estimation code pEst, developed at NASA Dryden, was used in this investigation. Results of the estimation process from alpha = 5 deg to alpha = 60 deg are presented and discussed.

Napolitano, Marcello R.↗