Search NASA⌕ Search

SEARCH · Search NASA

Results for “problem solving complexity”

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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Physics-informed neural networks (PINNs) for fluid mechanics: a review

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). Here, we demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.

42 ENGINEERING↗
NASA NTRS1997

Sequential Test Strategies for Multiple Fault Isolation

In this paper, we consider the problem of constructing near optimal test sequencing algorithms for diagnosing multiple faults in redundant (fault-tolerant) systems. The computational complexity of solving the optimal multiple-fault isolation problem is super-exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and Lagrangian relaxation, we present several static and dynamic (on-line or interactive) test sequencing algorithms for the multiple fault isolation problem that provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a static diagnostic directed graph (digraph), instead of a static diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. Computational results based on real-world systems indicate that the size of a static multiple fault strategy is strictly related to the structure of the system, and that the use of an on-line multiple fault strategy can diagnose faults in systems with as many as 10,000 failure sources.

Shakeri, M.↗
NASA NTRS1991

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility being the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements. Recent efforts have focused on reducing run time, improving accuracy and adding more boundary condition choices.

Klang, Eric C.↗
NASA NTRS1990

Shear buckling of specially orthotropic plates with centrally located cutouts

There is significant industry demand for a method of analyzing the shear buckling of composite plates with cutouts. This method should be able to easily accommodate frequent changes in model design; inflexibility is the major drawback to current finite element methods. The approach taken here is broken into two problems, prebuckling and buckling. To solve for the prebuckling stresses, complex variable equations are used in conjunction with boundary collocation. The least squares approach is utilized to improve the accuracy of the results. The buckling problem is solved using the Ritz method. A product of the Ritz method is a complicated integral equation which is solved using numerical integration. To date, the aforementioned method of determining the prebuckling stresses was verified against infinite plate theory and finite elements.

Owen, Vicki L.↗
NASA NTRS1988

GaussFit - A system for least squares and robust estimation

GaussFit is a new computer program for solving least-squares and robust estimation problems. It has a number of unique features, including a complete programming language designed especially to formulate estimation problems, a built-in compiler and interpreter to support the programming language, and a built-in algebraic manipulator for calculating the required partial derivatives analytically. These features make GaussFit very easy to use, so that even complex problems can be set up and solved with minimal effort. GaussFit can correctly handle many cases of practical interest: nonlinear models, exact constraints, correlated observations, and models where the equations of condition contain more than one observed quantity. An experimental robust estimation capability is built into GaussFit so that data sets contaminated by outliers can be handled simply and efficiently.

Jefferys, W. H.↗
NASA NTRS1995

An empirical evaluation of graphical interfaces to support flight planning

Whether optimization techniques or expert systems technologies are used, the underlying inference processes and the model or knowledge base for a computerized problem-solving system are likely to be incomplete for any given complex, real-world task. To deal with the resultant brittleness, it has been suggested that 'cooperative' rather than 'automated' problem-solving systems be designed. Such cooperative systems are proposed to explicitly enhance the collaboration of people and the computer system when working in partnership to solve problems. This study evaluates the impact of alternative design concepts on the performance of airline pilots interacting with such a cooperative system designed to support enroute flight planning. Thirty pilots were studied using three different versions of the system. The results clearly demonstrate that different system design concepts can strongly influence the cognitive processes of users. Indeed, one of the designs studied caused four times as many pilots to accept a poor flight amendment. Based on think-aloud protocols, cognitive models are proposed to account for how features of the computer system interacted with specific types of scenarios to influence exploration and decision-making by the pilots. The results are then used to develop recommendations for guiding the design of cooperative systems.

Smith, Philip J.↗
NASA NTRS1982

A transonic rectangular grid embedded panel method

A method is presented that has the potential for solving transonic flow problems about the same complex aircraft configurations currently being analyzed by subsonic panel methods. This method does not require the generation of surface fitted grids. Instead it uses rectangular grids and subgrids together with embedded surface panels on which boundary conditions are imposed. Both the Euler and full potential equations are considered. The method of least squares is used to reduce the solution of these equations to the solution of a sequence of Poisson problems. The Poisson problems are solved using fast Fourier transforms and panel influence coefficient techniques. The overall method is still in its infancy but some two dimensional results are shown illustrating various key features.

Johnson, F. T.↗
DOE OSTI2022

C3F: Collaborative Container-based Model Coupling Framework

Solving complex real-world grand challenge problems requires in-depth collaboration of researchers from multiple disciplines. Such collaboration often involves harnessing multiscale and multi-dimensional data and combining models from different fields to simulate systems. However, the progress on this front has been limited mainly due to significant gaps in domain knowledge and tools that are typically employed in silos of the domains. Researchers from different fields face considerable barriers to understanding and reusing each other’s data/models in order to collaborate effectively. For example, in solving the global sustainability problems, researchers from hydrology, climate science, agriculture, and economics need to run their respective models to study different components of the global and local food, energy and water systems while, at the same time, need to interact with other researchers and integrate the results of one model with another. Developing this kind of model coupling workflow calls for (1) a large amount of data being processed and exchanged across domains and organizations, (2) identifying and processing the output of one model to make it ready for integration into another model, (3) controlling the workflow dynamically so that it runs until a certain convergence condition or other criteria is met, and (4) close collaboration among the modelers to explore, tune, and test the configuration and data transformation needed to link the models. We have developed C3F, a flexible collaborative model coupling framework to help researchers accelerate their model integration and linking efforts by leveraging advanced cyberinfrastructure such as high-performance computing and virtual containers. In this paper, we describe our experience and lessons learned in developing this cyberinfrastructure solution to support the linking of Water Balance Model (WBM) and SIMPLE-G agricultural economic model in an NSF funded INFEWS project and a DOE-funded Program on Coupled Human and Earth Systems (PCHES) to study the implications of groundwater scarcity for food-energy-water systems. The C3F model coupling framework can be extended to facilitate other model linkages as well.

containerization↗
NASA NTRS1991

Determination of a natural basis function set on thick, structured slabs using Prony's method

The calculation of currents on a thick, structured slab such as a thick slab of honeycomb is discussed. Unfortunately, for certain applications, the slab can be on the order of several wavelengths, so that the straightforward application of the method of moments using subdomain basis functions is too expensive. The authors discuss how to apply Prony's method to the currents calculated for a thin, structured slab to obtain a natural set of basis functions to represent the currents in the interior of a thick slab. Prony's method represents the currents as a series of complex exponential functions. The thick slab problem is then solved by the method of moments using subdomain basis functions near the slab interfaces and one or two of the complex exponentials as basis functions within the slab.

Jorgenson, Roy E.↗
DOE OSTI2021

Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

In this study, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to generate. To reduce or even eliminate the dependency on high-fidelity data, we propose a novel multi-fidelity architecture which is based on a feature space shared by the low- and high-fidelity solutions. In the feature space, the projections of the low-fidelity and high-fidelity solutions are adjacent by constraining their relative distance. The feature space is represented with an encoder and its mapping to the original solution space is effected through a decoder. In conclusion, the proposed multi-fidelity approach is validated on forward and inverse problems for steady and unsteady problems described by partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still be challenging, often resulting in unsatisfactory accuracy and efficiency. In this work, we demonstrate that the failure of plain physics-informed neural networks arises from the significant discrepancy in the convergence rate of residuals at different training points, where the slowest convergence rate dominates the overall solution convergence. Based on these observations, we propose a pointwise adaptive weighting method that balances the residual decay rate across different training points. The performance of our proposed adaptive weighting method is compared with current state-of-the-art adaptive weighting methods on benchmark problems for both physics-informed neural networks and physics-informed deep operator networks. In conclusion, through extensive numerical results we demonstrate that our proposed approach of balanced residual decay rates offers several advantages, including bounded weights, high prediction accuracy, fast convergence rate, low training uncertainty, low computational cost, and ease of hyperparameter tuning.

Balanced convergence rate↗
DOE OSTI2024

ML-based Dimension Reduction Strategies

Deep learning (DL)--based surrogate models have achieved success in various applications in carbon capture and storage (CCS). However, the model training on high-dimensional spaces is computationally expensive and impractical for large-scale and complex geological models, because the models usually contain hundreds of thousands to millions of grid cells, each with a set of parameters. Furthermore, the high cost of generating training data with sufficient variation is another limitation of model training on high-dimensional spaces, which may result in overfitting and reduce the model efficiency and prediction performance. We proposed the workflow incorporating dimension reduction methods and deep learning models, which aim to extract the latent variables of input parameters and output state variables, and then build the mapping function at the latent spaces. The proposed workflow can significantly reduce the computational complexity in solving both forward and inverse problems compared to models trained on high-dimensional spaces. Dimensionality reduction models showed great potential in workflows for fast reservoir simulation, history matching, prior model generation, visualization, and more, ultimately enhancing DL model performance in related SMART Work Packages.

Hosseini, Seyyed↗
DOE OSTI2025

Applications of Federated Learning in Semiconductor Manufacturing [Poster]

As semiconductor manufacturers explore advanced data analytics and modeling techniques and data hungry machine learning models increase in popularity due to their accuracy in solving generalized problems and ability to learn complex relationships, federated learning emerges as a privacy preserving machine learning technique for preserving data privacy and ensuring intellectual property protection. Federated Learning is a machine learning technique focused on training models using distributed data that never needs to be centrally stored, allowing the use of advanced machine learning techniques without compromising data privacy, and in the semiconductor manufacturing industry advanced machine learning techniques can reduce cost and time, but maintaining data privacy is essential to maintaining a competitive advantage. This paper systematically reviews existing literature on applications of federated learning in the semiconductor manufacturing industry with a focus on identifying common themes, algorithms, and gaps within the literature to drive future research directions. The findings reveal five key themes, including improvements in quality assurance, virtual models, privacy preservation, reliable data practices, and emerging trends and developments. By identifying key themes in literature on federated learning and semiconductor manufacturing and analyzing gaps and discussed methodologies, this study highlights several potential future research directions to expand the application of federated learning techniques in the semiconductor manufacturing domain.

42 ENGINEERING↗
NASA NTRS1987

Expert systems for space power supply - Design, analysis, and evaluation

The feasibility of applying expert systems to the conceptual design, analysis, and evaluation of space power supplies in particular, and complex systems in general is evaluated. To do this, the space power supply design process and its associated knowledge base were analyzed and characterized in a form suitable for computer emulation of a human expert. The existing expert system tools and the results achieved with them were evaluated to assess their applicability to power system design. Some new concepts for combining program architectures (modular expert systems and algorithms) with information about the domain were applied to create a 'deep' system for handling the complex design problem. NOVICE, a code to solve a simplified version of a scoping study of a wide variety of power supply types for a broad range of missions, has been developed, programmed, and tested as a concrete feasibility demonstration.

Cooper, Ralph S.↗
NASA NTRS1992

CSM activities at the NASA Langley Research Center

The objective and goals of the Computational Structural Mechanics (CSM) Program as applied to airframe structures are given. It is recognized that the rapid evolution of computer hardware has opened up new opportunities for solving more complex and larger structural analysis problems than was hitherto imagined. To utilize these computers, new methods of computational structural mechanics are required. Methods are now being developed, assessed, and validated to meet the goals, and each of these goals is addressed. Plans and approaches are shown and highlights of results achieved in meeting these goals are given. Three research thrusts are shown in the five-year plan: advanced robust CSM methods, large-scale solutions, and validation/demonstration studies. The areas of research activity reflect the CSM goals. The mapping of developed methods onto high-performance and massively parallel computers is an integral part of the CSM five-year plan.

Housner, Jerrold M.↗
NASA NTRS1992

Materials surface contamination analysis

The original research objective was to demonstrate the ability of optical fiber spectrometry to determine contamination levels on solid rocket motor cases in order to identify surface conditions which may result in poor bonds during production. The capability of using the spectral features to identify contaminants with other sensors which might only indicate a potential contamination level provides a real enhancement to current inspection systems such as Optical Stimulated Electron Emission (OSEE). The optical fiber probe can easily fit into the same scanning fixtures as the OSEE. The initial data obtained using the Guided Wave Model 260 spectrophotometer was primarily focused on determining spectra of potential contaminants such as HD2 grease, silicones, etc. However, once we began taking data and applying multivariate analysis techniques, using a program that can handle very large data sets, i.e., Unscrambler 2, it became apparent that the techniques also might provide a nice scientific tool for determining oxidation and chemisorption rates under controlled conditions. As the ultimate power of the technique became recognized, considering that the chemical system which was most frequently studied in this work is water + D6AC steel, we became very interested in trying the spectroscopic techniques to solve a broad range of problems. The complexity of the observed spectra for the D6AC + water system is due to overlaps between the water peaks, the resulting chemisorbed species, and products of reaction which also contain OH stretching bands. Unscrambling these spectral features, without knowledge of the specific species involved, has proven to be a formidable task.

Workman, Gary L.↗
NASA NTRS1997

RIACS

Topics considered include: high-performance computing; cognitive and perceptual prostheses (computational aids designed to leverage human abilities); autonomous systems. Also included: development of a 3D unstructured grid code based on a finite volume formulation and applied to the Navier-stokes equations; Cartesian grid methods for complex geometry; multigrid methods for solving elliptic problems on unstructured grids; algebraic non-overlapping domain decomposition methods for compressible fluid flow problems on unstructured meshes; numerical methods for the compressible navier-stokes equations with application to aerodynamic flows; research in aerodynamic shape optimization; S-HARP: a parallel dynamic spectral partitioner; numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains; application of high-order shock capturing schemes to direct simulation of turbulence; multicast technology; network testbeds; supercomputer consolidation project.

Oliger, Joseph↗