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DOE OSTI2024

Task-oriented machine learning surrogates for tipping points of agent-based models

We present a machine learning framework bridging manifold learning, neural networks, Gaussian processes, and Equation-Free multiscale approach, for the construction of different types of effective reduced order models from detailed agent-based simulators and the systematic multiscale numerical analysis of their emergent dynamics. The specific tasks of interest here include the detection of tipping points, and the uncertainty quantification of rare events near them. Our illustrative examples are an event-driven, stochastic financial market model describing the mimetic behavior of traders, and a compartmental stochastic epidemic model on an Erdös-Rényi network. We contrast the pros and cons of the different types of surrogate models and the effort involved in learning them. Importantly, the proposed framework reveals that, around the tipping points, the emergent dynamics of both benchmark examples can be effectively described by a one-dimensional stochastic differential equation, thus revealing the intrinsic dimensionality of the normal form of the specific type of the tipping point. This allows a significant reduction in the computational cost of the tasks of interest.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1981

The design and development of a mixer compound exhaust system for a quiet clean general aviation turbofan

Lower engine fuel consumption has become a dominant factor in turbofan engine design due to rapidly increasing fuel costs. One engine component with a large impact on engine performance is the exhaust system. Previous exhaust system studies have demonstrated the significant exhaust system efficiency gains available through mixing of the core and bypass flows. Typically, a large, costly rig and engine program are required to develop and optimize these gains. The purpose of this paper is to present the results of the low-cost design system used for the quiet, clean general aviation turbofan mixer nozzle design and development. The scale model and full-scale engine test results confirm the predicted 3 to 5% reduction in cruise fuel consumption. This unique design system, which is based on integrating advanced three-dimensional viscous numerical methods with empirical optimization techniques, is summarized and detailed comparisons with test data are presented. The ability to accurately predict relative performance of mixer systems with substantially reduced development time and cost savings is demonstrated.

Blackmore, W. L.↗

NASA NTRS1990

Influence of local configuration on the backflow from small rocket thrusters

A numerical study has been made of the low density plume flow from a small thruster motor. For the case studied, the addition of a thin plume shield with a diameter 1.67 times the nozzle exit diameter was found to lead to a reduction in the backflow by several orders of magnitude. Calculations were also made for the three-dimensional flow produced by a pair of motors, in order to determine the increase in the backflow due to the interaction of the plumes. The calculations were made with the direct simulation Monte Carlo (DSMC) method, and one of the purposes of the work was to test a new and faster set of algorithms for this method.

Bird, G. A.↗

NASA NTRS2004

Effect of Assumed Damage and Location on the Delamination Onset Predictions for Skin-Stiffener Debonding

The difference in delamination onset predictions based on the type and location of the assumed initial damage are compared in a specimen consisting of a tapered flange laminate bonded to a skin laminate. From previous experimental work, the damage was identified to consist of a matrix crack in the top skin layer followed by a delamination between the top and second skin layer (+45 deg./-45 deg. interface). Two-dimensional finite elements analyses were performed for three different assumed flaws and the results show a considerable reduction in critical load if an initial delamination is assumed to be present, both under tension and bending loads. For a crack length corresponding to the peak in the strain energy release rate, the delamination onset load for an assumed initial flaw in the bondline is slightly higher than the critical load for delamination onset from an assumed skin matrix crack, both under tension and bending loads. As a result, assuming an initial flaw in the bondline is simpler while providing a critical load relatively close to the real case. For the configuration studied, a small delamination might form at a lower tension load than the critical load calculated for a 12.7 mm (0.5") delamination, but it would grow in a stable manner. For the bending case, assuming an initial flaw of 12.7 mm (0.5") is conservative, the crack would grow unstably.

Paris, Isabelle L.↗

NASA NTRS1994

Probing the antiferromagnetic long-range order with Glauber spin states

It is well known that the ground state of low-dimensional antiferromagnets deviates from Neel states due to strong quantum fluctuations. Even in the presence of long-range order, those fluctuations produce a substantial reduction of the magnetic moment from its saturation value. Numerical simulations in anisotropic antiferromagnetic chains suggest that quantum fluctuations over Neel order appear in the form of localized reversal of pairs of neighboring spins. In this paper, we propose a coherent state representation for the ground state to describe the above situation. In the one-dimensional case, our wave function corresponds to a two-mode Glauber state, when the Neel state is used as a reference, while the boson fields are associated to coherent flip of spin pairs. The coherence manifests itself through the antiferromagnetic long-range order that survives the action of quantum fluctuations. The present representation is different from the standard zero-point spin wave state, and is asymptotically exact in the limit of strong anisotropy. The fermionic version of the theory, obtained through the Jordan-Wigner transformation, is also investigated.

Cabrera, Guillermo G.↗

NASA NTRS2007

Polymer-Layered Silicate Nanocomposites for Cryotank Applications

Previous composite cryotank designs have relied on the use of conventional composite materials to reduce microcracking and permeability. However, revolutionary advances in nanotechnology derived materials may enable the production of ultra-lightweight cryotanks with significantly enhanced durability and damage tolerance, as well as reduced propellant permeability. Layered silicate nanocomposites are especially attractive in cryogenic storage tanks based on results that have been reported for epoxy nanocomposite systems. These materials often exhibit an order of magnitude reduction in gas permeability when compared to the base resin. In addition, polymer-silicate nanocomposites have been shown to yield improved dimensional stability, strength, and toughness. The enhancement in material performance of these systems occurs without property trade-offs which are often observed in conventionally filled polymer composites. Research efforts at NASA Glenn Research Center have led to the development of epoxy-clay nanocomposites with 70% lower hydrogen permeability than the base epoxy resin. Filament wound carbon fiber reinforced tanks made with this nanocomposite had a five-fold lower helium leak rate than the corresponding tanks made without clay. The pronounced reduction observed with the tank may be due to flow induced alignment of the clay layers during processing. Additionally, the nanocomposites showed CTE reductions of up to 30%, as well as a 100% increase in toughness.

Miller, Sandi G.↗

NASA NTRS1987

Method of thermal strain hysteresis reduction in metal matrix composites

A method is disclosed for treating graphite reinforced metal matrix composites so as to eliminate thermal strain hysteresis and impart dimensional stability through a large thermal cycle. The method is applied to the composite post fabrication and is effective on metal matrix materials using graphite fibers manufactured by both the hot roll bonding and diffusion bonding techniques. The method consists of first heat treating the material in a solution anneal oven followed by a water quench and then subjecting the material to a cryogenic treatment in a cryogenic oven. This heat treatment and cryogenic stress reflief is effective in imparting a dimensional stability and reduced thermal strain hysteresis in the material over a -250.degree. F. to +250.degree. F. thermal cycle.

Dries, Gregory A.↗

NASA NTRS1973

Application of phase-change technique to thin sections with heating on both surfaces

A numerical digital computer program was developed to calculate the heat-transfer coefficients for both sides of a one-dimensional finite slab subject to the boundary conditions ascribed to the phase-change coating heat-transfer technique. In a typical tunnel test situation where a thin wing was exposed to heating on both sides, the data reduction procedures for a semi-infinite slab gave heat-transfer coefficients as much as 375 percent too high on the side with the lowest heating. The results from the one-dimensional finite-slab procedure are presented in the form of correction factors to the solution for a semi-infinite slab in terms of parameters normally used with the phase-change heat-transfer technique. These correlations are not restricted to slab thickness or thermophysical properties and are easily used to obtain accurate data on thin model sections.

Hunt, J. L.↗

NASA NTRS1983

Aerodynamic design for improved maneuverability by the use of three-dimensional transonic theory

This study has examined the level of transonic maneuver performance that can be achieved by the use of three-dimensional transonic theory. The FLO-27 code of Jameson and Caughey (1977) was used to lower maneuver drag by the reduction of shock strength on the wing upper surface. A design procedure was used to provide a set of guidelines for the iterative application of FLO-27 during the wing design process. The fighter configuration utilized had a leading-edge sweep of 45 deg and an aspect ratio of 3.28. Tests were conducted at Mach numbers from 0.60 to 0.95 and angles of attack from -5 to 18 deg. The accurate prediction of wing shock systems required the inclusion of fuselage effects in the theory. The FLO-27 code gave a reasonable estimate of the experimental wing pressure distributions at transonic maneuver conditions in the region of the wing where the flow was attached. For Mach numbers between 0.60 and 0.95 and lift coefficients near 0.9, a wing designed by the use of FLO-27 showed substantially lower drag than an empirically developed, supercritical maneuver wing and a maneuver wing designed primarily by two-dimensional transonic theory. For some maneuver conditions, the drag of the two-dimensional design was somewhat lower.

Mann, M. J.↗

DOE OSTI2024

Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification

The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Structural optimization of turbine blade firtrees

On the basis of the present optimization equation for the structural capacity of a turbine blade attachment firtree, the optimum of the lobe circular fillet radius in the blade and in the turbine disk is determined. In order to further diminish peak stress in firtree design, an elliptical fillet radius is selected in place of the circular one. Two-dimensional stress analysis results for a three-lobe firtree with elliptical radius shows a 14-percent stress reduction in the blade necks (where cracking has been experienced) over the current, four-lobe firtree design.

Lee, R. L.↗

NASA NTRS1991

Combined magnetic vector-scalar potential finite element computation of 3D magnetic field and performance of modified Lundell alternators in Space Station applications

A method of combined use of magnetic vector potential (MVP) based finite element (FE) formulations and magnetic scalar potential (MSP) based FE formulations for computation of three-dimensional (3D) magnetostatic fields is developed. This combined MVP-MSP 3D-FE method leads to considerable reduction by nearly a factor of 3 in the number of unknowns in comparison to the number of unknowns which must be computed in global MVP based FE solutions. This method allows one to incorporate portions of iron cores sandwiched in between coils (conductors) in current-carrying regions. Thus, it greatly simplifies the geometries of current carrying regions (in comparison with the exclusive MSP based methods) in electric machinery applications. A unique feature of this approach is that the global MSP solution is single valued in nature, that is, no branch cut is needed. This is again a superiority over the exclusive MSP based methods. A Newton-Raphson procedure with a concept of an adaptive relaxation factor was developed and successfully used in solving the 3D-FE problem with magnetic material anisotropy and nonlinearity. Accordingly, this combined MVP-MSP 3D-FE method is most suited for solution of large scale global type magnetic field computations in rotating electric machinery with very complex magnetic circuit geometries, as well as nonlinear and anisotropic material properties.

Wang, Ren H.↗

NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗

NASA NTRS1993

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Jiang, Yi-Tsann↗

NASA NTRS1992

Extracting galactic structure parameters from multivariated density estimation

Multivariate statistical analysis, including includes cluster analysis (unsupervised classification), discriminant analysis (supervised classification) and principle component analysis (dimensionlity reduction method), and nonparameter density estimation have been successfully used to search for meaningful associations in the 5-dimensional space of observables between observed points and the sets of simulated points generated from a synthetic approach of galaxy modelling. These methodologies can be applied as the new tools to obtain information about hidden structure otherwise unrecognizable, and place important constraints on the space distribution of various stellar populations in the Milky Way. In this paper, we concentrate on illustrating how to use nonparameter density estimation to substitute for the true densities in both of the simulating sample and real sample in the five-dimensional space. In order to fit model predicted densities to reality, we derive a set of equations which include n lines (where n is the total number of observed points) and m (where m: the numbers of predefined groups) unknown parameters. A least-square estimation will allow us to determine the density law of different groups and components in the Galaxy. The output from our software, which can be used in many research fields, will also give out the systematic error between the model and the observation by a Bayes rule.

Chen, B.↗

NASA NTRS1994

Interpretation of satellite airglow observations during the March 22, 1979, magnetic storm, using the coupled ionosphere-thermosphere model developed at University College, London

The University of California, Berkeley, extreme ultraviolet spectrometer aboard the U.S. Air Force STP 78-1 satellite measured emission features in the Earth's dayglow due to neutral and ionized species in the atmosphere, in the 35 to 140-nm range. The spectrometer was operating between March 1979 and March 1980, including the period of the magnetic storm on March 22, 1979. Some of these measurements are interpreted using the predictions of the three-dimensional time-dependent coupled ionosphere-thermosphere model developed at University College, London. The observations show a reduction in the atomic oxygen 130.4-nm airglow emission at high northern latitudes following the storm. Model simulations show that this reduction in 130.4-nm emission is associated with an increase in the O2/O ratio. Analysis of model results using electron transport and radiative transport codes show that the brightness of 130.4-nm emission at high latitudes due to resonantly scattered sunlight is approximately twice that due to photoelectron impact excitation. However, the observed decrease in the brightness at high northern latitudes is mainly due to a change in the photoelectron impact source, which contributes approximately 75% of the total, as well as its multiple scattering component; for the photoelectron impact source at 70 deg latitude and 200 km altitude, the reduction in multiple scattering is 1.5 times greater than the reduction in the initial excitation. The reduction in the airglow emission is visible only in the norther n hemisphere because the south pole was not sunlit over the storm period. The comparison of model results with observations suggests that 130.4-nm emission may be useful as a tracer for global changes in the concentration of atomic energy.

Parish, H. F.↗

NASA NTRS1999

Decimated Input Ensembles for Improved Generalization

Recently, many researchers have demonstrated that using classifier ensembles (e.g., averaging the outputs of multiple classifiers before reaching a classification decision) leads to improved performance for many difficult generalization problems. However, in many domains there are serious impediments to such "turnkey" classification accuracy improvements. Most notable among these is the deleterious effect of highly correlated classifiers on the ensemble performance. One particular solution to this problem is generating "new" training sets by sampling the original one. However, with finite number of patterns, this causes a reduction in the training patterns each classifier sees, often resulting in considerably worsened generalization performance (particularly for high dimensional data domains) for each individual classifier. Generally, this drop in the accuracy of the individual classifier performance more than offsets any potential gains due to combining, unless diversity among classifiers is actively promoted. In this work, we introduce a method that: (1) reduces the correlation among the classifiers; (2) reduces the dimensionality of the data, thus lessening the impact of the 'curse of dimensionality'; and (3) improves the classification performance of the ensemble.

Tumer, Kagan↗

NASA NTRS2015

M2 Internal Tides and Their Observed Wavenumber Spectra from Satellite Altimetry*

A near-global chart of surface elevations associated with the stationary M2 internal tide is empirically constructed from multi-mission satellite altimeter data. An advantage of a strictly empirical mapping approach is that results are independent of assumptions about ocean wave dynamics and, in fact, can be used to test such assumptions. A disadvantage is that present-day altimeter coverage is only marginally adequate to support mapping such short-wavelength features. Moreover, predominantly north-south ground-track orientations and contamination from nontidal oceanographic variability can lead to deficiencies in mapped tides. Independent data from Cryosphere Satellite-2 (CryoSat-2) and other altimeters are used to test the solutions and show positive reduction in variance except in regions of large mesoscale variability. The tidal fields are subjected to two-dimensional wavenumber spectral analysis, which allows for the construction of an empirical map of modal wavelengths. Mode-1 wavelengths show good agreement with theoretical wavelengths calculated from the ocean's mean stratification, with a few localized exceptions (e.g., Tasman Sea). Mode-2 waves are detectable in much of the ocean, with wavelengths in reasonable agreement with theoretical expectations, but their spectral signatures grow too weak to map in some regions.

Ray, R. D.↗