SEARCH · Search NASA

Results for “model structural error”

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.

SourceResearch connectionFrom yearThrough year

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

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2026

Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study

Neural scaling laws play a pivotal role in the performance of deep neural networks and have been observed in a wide range of tasks. However, a complete theoretical framework for understanding these scaling laws remains underdeveloped. In this paper, we explore the neural scaling laws for deep operator networks, which involve learning mappings between function spaces, with a focus on the Chen and Chen style architecture. These approaches, which include the popular Deep Operator Network (DeepONet), approximate the output functions using a linear combination of learnable basis functions and coefficients that depend on the input functions. We establish a theoretical framework to quantify the neural scaling laws by analyzing its approximation and generalization errors. We articulate the relationship between the approximation and generalization errors of deep operator networks and key factors such as network model size and training data size. Moreover, we address cases where input functions exhibit low-dimensional structures, allowing us to derive tighter error bounds. These results also hold for deep ReLU networks and other similar structures. Our results offer a partial explanation of the neural scaling laws in operator learning and provide a theoretical foundation for their applications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Experimental measurement and theoretical modeling of microwave scattering and the structure of the sea surface influencing radar observations from space

The electromagnetic (EM) bias 'epsilon' is an error present in radar altimetry of the ocean due to the nonuniform reflection from wave troughs and crests. The EM bias is defined as the difference between the mean reflecting surface and the mean sea surface. A knowledge of the EM bias is necessary to permit error reduction in mean sea level measurements by satellite radar altimeters. Direct measurements of the EM bias were made from a Shell Offshore oil production platform in the Gulf of Mexico for a six month period during 1989 and 1990. Measurements of the EM bias were made at 5 and 14 Ghz. During the EM bias experiments by Melville et al., a wire wave gauge was used to obtain the modulation of the high frequency waves by the low frequency waves. It became apparent that the EM bias was primarily caused by the modulation of the short waves. This was reported by Arnold et al. The EM bias is explained using physical optics scattering and an empirical model for the short wave modulation. Measurements of the short wave modulation using a wire wave gauge demonstrated a linear dependence of the normalized bias on the short wave modulation strength, M. The theory accurately predicts this dependence by the relation epsilon = -alphaMH sub 1/3. The wind speed dependence of the normalized bias is explained by the dependence of the short wave modulation strength on the wind speed. While other effects such as long wave tilt and curvature will have an effect on the bias, the primary cause of the bias is shown to be due to the short wave modulation. This report will present a theory using physical optics scattering and an empirical model of the short wave modulation to estimate the EM bias. The estimated EM bias will be compared to measurements at C and Ku bands.

Arnold, David↗

NASA NTRS1990

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗

NASA NTRS1995

Radial alignment simulation of solar wind streams observed by Pioneers 10 and 11 in 1974

A particularly favorable radial lineup between spacecraft in Earth orbit and Pioneers 10 and 11 (near the ecliptic plane at approximately 5.5 AU and approximately 4.5 AU, respectively) occurred in mid-1974, when the solar corona was in a stable and well-defined warped-dipole configuration. The radial alignment study reported here differs from previous applications of the technique in two respects: (1) It is the first time a two-dimensional (2-D) MHD model has been tested over such a lengthy propagation interval; the 2-D capability is crucial for treatment of the nonradial shearing motions occurring across the stream interface. (2) The three-dimensional (3-D) structure observed in the white light corona at that time is related to the systematic patterns of nonradial flow deflections appearing at the Pioneer corotating interaction region (CIR) fronts. Comparison of predicted and observed flows for pairs of streams in two successive rotations reveals that when the parent coronal hole projects far across the solar equator in a predominantly north-south orientation (i.e., nearest the 2-D idealization), the mapping is accurate down to details of the flow structures. But where the spacecraft tracks along a latitudinal boundary of a hole or the associated stream front is inclined at a shallow angle to the equator, the numerical projections deviate systematically from the observations. Among the sources of error are 3-D dynamical interactions neglected in the model, differential rotation effects, and slow temporal evolution of the coronal structures. A characteristic pattern of north-south and east-west deflections indicative of the 3-D geometry appears across the CIRs, but these patterns evidently reflect primarily the local, as opposed to global, orientation of the 3-D stream fronts. Such patterns appear common in CIRs observed by Pioneer during this period. These findings thus hold special relevance for the analysis of Ulysses observations, since the present coronal configuration is similar to that of 1974.

Pizzo, V. J.↗

NASA NTRS1986

Analysis of modeling errors in system identification

This paper is concerned with the identification of a system in the presence of several error sources. Following some basic definitions, the notion of 'near-equivalence in probability' is introduced using the concept of near-equivalence between a model and process. Necessary and sufficient conditions for the identifiability of system parameters are given. The effect of structural error on the parameter estimates for both deterministic and stochastic cases are considered.

Hadaegh, F. Y.↗

NASA NTRS2013

Analysis of a Split-Plot Experimental Design Applied to a Low-Speed Wind Tunnel Investigation

A procedure to analyze a split-plot experimental design featuring two input factors, two levels of randomization, and two error structures in a low-speed wind tunnel investigation of a small-scale model of a fighter airplane configuration is described in this report. Standard commercially-available statistical software was used to analyze the test results obtained in a randomization-restricted environment often encountered in wind tunnel testing. The input factors were differential horizontal stabilizer incidence and the angle of attack. The response variables were the aerodynamic coefficients of lift, drag, and pitching moment. Using split-plot terminology, the whole plot, or difficult-to-change, factor was the differential horizontal stabilizer incidence, and the subplot, or easy-to-change, factor was the angle of attack. The whole plot and subplot factors were both tested at three levels. Degrees of freedom for the whole plot error were provided by replication in the form of three blocks, or replicates, which were intended to simulate three consecutive days of wind tunnel facility operation. The analysis was conducted in three stages, which yielded the estimated mean squares, multiple regression function coefficients, and corresponding tests of significance for all individual terms at the whole plot and subplot levels for the three aerodynamic response variables. The estimated regression functions included main effects and two-factor interaction for the lift coefficient, main effects, two-factor interaction, and quadratic effects for the drag coefficient, and only main effects for the pitching moment coefficient.

Erickson, Gary E.↗

NASA NTRS1990

Thermal-distortion analysis of a spacecraft box truss in geostationary orbit

The Mission to Planet Earth enlists the use of a geostationary platform to support Earth science monitoring instruments. The strongback for a proposed geostationary platform is a deployable box truss that supports two large diameter passive microwave radiometer (PMR) and several other science instruments. A study was performed to estimate the north-south and east-west pointing errors at the mounting locations of the two PMRs due to on-orbit thermal distortions of the main truss. The baseline configuration indicated that the east-west pointing error greatly exceeded the required limits. Primary origins of the pointing errors were identified, and methods for their reduction were discussed. Thermal performance enhancements to the truss structure were modeled and analyzed, including state-of-the-art surface coatings and insulation techniques. Comparisons of the thermal enhancements to the baseline were performed. Results demonstrated that using a thermal enclosure insulating technique reduced external heat fluxes, and distributed those heat fluxes more evenly throughout the structure, sufficiently reducing the pointing error to satisfy pointing accuracy requirements for the PMR's.

Cosgrove, Patrick A.↗

DOE OSTI2024

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics↗

DOE OSTI2019

SubKit

Generating a CTF (thermal-hydraulics subchannel code) model can be time consuming and error prone because of the rigid formatting of the input file and the amount of input requirements. Because of the structured input format, making small changes to a model can require large scale changes to the input file. Furthermore, a user typically has to perform calculations to develop CTF input parameters from actual model geometry. Changing model geometry requires re-calculating input parameters and copying them from wherever the calculation was performed, be it a script, spreadsheet, or piece of paper. This process complicates the quality assurance process for that model and makes changing the model more difficult. CtfDeckBuilder is an object-oriented Python interface to CTF that allows the user to build a CTF model in Python. The user no longer needs to interface with the CTF input file when using the CtfDeckBuilder. The interface reduces the information required of the user by offering defaults for most modeling options provided by CTF. The user can perform calculations directly in Python when building the model so that calculations stay with the model itself.

Salko, Jr., RobertK↗

NASA NTRS2012

Understanding Shock Dynamics in the Inner Heliosphere with Modeling and Type II Radio Data: the 2010-04-03 Event

The 2010 April 03 solar event was studied using observations from STEREO SECCHI, SOHO LASCO, and Wind kilometric Type II data (kmTII) combined with WSA-Cone-ENLIL model simulations performed at the Community Coordinated Modeling Center (CCMC). In particular, we identified the origin of the coronal mass ejection (CME) using STEREO EUVI and SOHO EIT images. A flux-rope model was fit to the SECCHI A and B, and LASCO images to determine the CMEs direction, size, and actual speed. J-maps from STEREO COR2HI-1HI-2 and simulations fromCCMC were used to study the formation and evolution of the shock in the inner heliosphere. In addition, we also studied the time-distance profile of the shock propagation from kmTII radio burst observations. The J-maps together with in-situ datafrom the Wind spacecraft provided an opportunity to validate the simulation results andthe kmTII prediction. Here we report on a comparison of two methods of predictinginterplanetary shock arrival time: the ENLIL model and the kmTII method; andinvestigate whether or not using the ENLIL model density improves the kmTIIprediction. We found that the ENLIL model predicted the kinematics of shock evolutionwell. The shock arrival times (SAT) and linear-fit shock velocities in the ENLILmodel agreed well with those measurements in the J-maps along both the CME leading edge and the Sun-Earth line. The ENLIL model also reproduced most of the largescale structures of the shock propagation and gave the SAT prediction at Earth with an error of 17 hours. The kmTII method predicted the SAT at Earth with an error of 15 hours when using n0 4.16 cm3, the ENLIL model plasma density near Earth; but itimproved to 2 hours when using n0 6.64 cm3, the model density near the CMEleading edge at 1 AU.

Space weather forecast↗

NASA NTRS1988

ACES program - Lessons learned

The ACES Program involved the experimental evaluation of three LSS (large space structures) control design techniques at the LSS GTF (ground test facility) at NASA/MSFC. The three techniques were developed under the ACOSS (active control of space structures) Program specifically for application to LSS. The techniques included FAMESS (filter accommodated model error sensitivity suppression), HAC/LAC (high authority control/low authority control), and positivity. Some of the lessons that have been learned during the course of the ACES program are examined.

Jones, Victoria L.↗

NASA NTRS1997

A Presentation on Robust Flutter Margin Analysis and a Flutterometer

This paper documents an invited presentation given to The Boeing Company, Seattle, Washington, on September 9, 1997. The audience consisted of structural dynamic and flight test engineers from the Boeing Commercial Airplane Group who were interested in discussing research which may be applied to future flight flutter test programs. A method to compute robust flutter margins is described which is a significant departure from traditional methods. This method uses the structured singular value, mu, to compute a flutter margin which directly accounts for modeling errors such that a worst-case flutter margin is computed with respect to those errors. This method may be applied in several ways. A post-flight application uses data sets from multiple test points to compute worst-case flutter margins and a worst-case flight envelope. An on-line implementation computes flutter margins at each test point to track the flutter margins during a flight test. This on-line implementation is the basis for a flutterometer flight test tool that displays the distance to flutter at a given test point. Such a tool was not previously possible using traditional flutter flight test analysis methods. The F/A-18 System Research Aircraft was used to demonstrate these applications using flight data recorded from test points throughout the flight envelope.

Lind, Rick C.↗

NASA NTRS2004

Performance and Reliability Optimization for Aerospace Systems subject to Uncertainty and Degradation

This report summarizes work performed by the Space Systems Laboratory (SSL) for NASA Langley Research Center in the field of performance optimization for systems subject to uncertainty. The objective of the research is to develop design methods and tools to the aerospace vehicle design process which take into account lifecycle uncertainties. It recognizes that uncertainty between the predictions of integrated models and data collected from the system in its operational environment is unavoidable. Given the presence of uncertainty, the goal of this work is to develop means of identifying critical sources of uncertainty, and to combine these with the analytical tools used with integrated modeling. In this manner, system uncertainty analysis becomes part of the design process, and can motivate redesign. The specific program objectives were: 1. To incorporate uncertainty modeling, propagation and analysis into the integrated (controls, structures, payloads, disturbances, etc.) design process to derive the error bars associated with performance predictions. 2. To apply modern optimization tools to guide in the expenditure of funds in a way that most cost-effectively improves the lifecycle productivity of the system by enhancing the subsystem reliability and redundancy. The results from the second program objective are described. This report describes the work and results for the first objective: uncertainty modeling, propagation, and synthesis with integrated modeling.

Miller, David W.↗

DOE OSTI2022

Stability Analysis of Substituted Cobaltocenium [Bis(cyclopentadienyl)cobalt(III)] Employing Chemistry-Informed Neural Networks

Cobaltocenium derivatives are promising components of the anion exchange membranes due to their excellent thermal and alkaline stability under the operating conditions of a fuel cell. Here we present an efficient modeling approach of assessing the chemical stability of substituted cobaltocenium CoCp 2 + based on the computed electronic structure enhanced by machine learning techniques. Within the aqueous environment, the positive charge of the metal cation is balanced by the hydroxide anion through formation of the CoCp 2 + OH¯ complexes, whose dissociation is studied within the implicit solvent employing density functional theory. The data set of about 118 species based on 42 substituent groups characterized by a range of electron- donating (ED) and electron-withdrawing (EW) properties is constructed and analyzed. Given 12 carefully chosen chemistry-informed descriptors of the complexes and relevant fragments, the stability of the complexes is found to strongly correlate with the energies of the highest occupied and lowest unoccupied molecular orbitals, modulated by a switching function of the Hirshfeld charge. The latter is used as a measure of the electron withdrawing-donating character of the substituents. Based on this observation from the conventional regression analysis, two fully connected, feed-forward neural network (FNN) models with different unit structures, called the chemistry-informed (CINN) and the quadratic (QNN) neural networks, are developed. Both models predict the bond dissociation energies of the cobaltocenium complexes with mean relative errors less than 5.40% and average absolute errors less than 0.94 kcal/mol. The results show the potential of QNN to efficiently capture more complex relationships. Here, the concept of incorporating the domain (chemical) knowledge/insight into the neural network structure paves the way to applications of machine learning techniques with small data sets, ultimately leading to better predictive models compared to the conventional regression analysis.

36 MATERIALS SCIENCE↗

NASA NTRS1982

Evaluation and reduction of errors induced by the Guyan transformation

The Guyan reduction refers to a method used to reduce the number of degrees of freedom in a structural model for dynamic analysis. Experience shows that, if the method is properly employed, then this reduction method does in fact provide a "reasonably" accurate approximation of the dynamic characteristics of the unreduced model. A method that provides an accurate estimate of the error in each mode of the reduced eigenvalue problem and, in addition, gives first order correction terms that greatly improve the accuracy of the eigenvectors and eigenvalues is presented. The method is demonstrated by standard COSMIC NASTRAN DAMP alters to rigid format 3, real normal mode analysis. Comparative computer time of modal extraction versus error analysis is discussed for the VAX-11/780 version of COSMIC NASTRAN.

Fox, G. L.↗

DOE OSTI2023

Assessing Clouds Using Satellite Observations Through Three Generations of Global Atmosphere Models

Abstract Clouds are parameterized in climate models using quantities on the model grid‐scale to approximate the cloud cover and impact on radiation. Because of the complexity of processes involved with clouds, these parameterizations are one of the key challenges in climate modeling. Differences in parameterizations of clouds are among the main contributors to the spread in climate sensitivity across models. In this work, the clouds in three generations of an atmosphere model lineage are evaluated against satellite observations. Satellite simulators are used within the model to provide an appropriate comparison with individual satellite products. In some respects, especially the top‐of‐atmosphere cloud radiative effect, the models show generational improvements. The most recent generation, represented by two distinct branches of development, exhibits some regional regressions in the cloud representation; in particular the southern ocean shows a positive bias in cloud cover. The two branches of model development show how choices during model development, both structural and parametric, lead to different cloud climatologies. Several evaluation strategies are used to quantify the spatial errors in terms of the large‐scale circulation and the cloud structure. The Earth mover's distance is proposed as a useful error metric for the passive satellite data products that provide cloud‐top pressure‐optical depth histograms. The cloud errors identified here may contribute to the high climate sensitivity in the Community Earth System Model, version 2 and in the Energy Exascale Earth System Model, version 1.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Analytic error analysis of cross section interpolation methods in nodal diffusion codes - I : Theory

This paper discusses two cross section interpolation methods commonly found in popular nodal codes; the partial derivatives and multiple tables models. The motivation for choosing a model, and thus a case matrix structure, is a trade off between accuracy and computational cost. Due to decades of experience, there are default structures that are sufficient for current light water reactor analysis. However, this is not necessarily the case for advanced reactor designs. Therefore, it is advantageous to understand the sources of error in cross section interpolation models so that the quality of a case matrix may be improved. A mathematical framework for these models is presented in this work that provides a more rigorous connection between the nuclear engineering field's cross section interpolation methods and the broader mathematical field of function approximation. The two cross section models examined in this paper were found to utilize Lagrange interpolation and are a subset of Lagrange tensor products. Classical results of Lagrange polynomial error analysis were then applied to the partial derivative and multiple tables models to derive expressions for the total point-wise error. The analytical results classify the total error into two parts: the model form error and interpolation error. Finally, based on our observations, a better foundation for improving the quality of a case matrix is proposed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Quantifying correlated truncation errors in effective field theory

Effective field theories (EFTs) organize the description of complex systems into an infinite sequence of decreasing importance. Predictions are made with a finite number of terms, which induces a truncation error that is often left unquantified. Here, we formalize the notion of EFT convergence and propose a Bayesian truncation error model for predictions that are correlated across the independent variables, e.g., energy or scattering angle. Central to our approach are Gaussian processes that encode both the naturalness and correlation structure of EFT coefficients. Our use of Gaussian processes permits efficient and accurate assessment of credible intervals, allows EFT fits to easily include correlated theory errors, and provides analytic posteriors for physical EFT-related quantities such as the expansion parameter. Furthermore, we demonstrate that model-checking diagnostics—applied to the case of multiple curves—are powerful tools for EFT validation. As an example, we assess a set of nucleon-nucleon scattering observables in chiral EFT. In an effort to be self-contained, appendices include thorough derivations of our statistical results. Our methods are packaged in Python code, called gsum, that is available for download on GitHub.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗