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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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NASA NTRS1990

Image construction from the IRAS survey and data fusion

The IRAS survey data can be used successfully to produce images of extended objects. The major difficulty, viz. non-uniform sampling, different response functions for each detector, and varying signal-to-noise levels for each detector for each scan, were resolved. The results of three different image construction techniques are compared: co-addition, constrained least squares, and maximum entropy. The maximum entropy result is superior. An image of the galaxy M51 with an average spatial resolution of 45 arc seconds, is presented using 60 micron survey data. This exceeds the telescope diffraction limit of 1 minute of arc, at this wavelength. Data fusion is a proposed method for combining data from different instruments, with different spatial resolutions, at different wavelengths. Direct estimates of the physical parameters, temperature, density and composition, can be made from the data without prior images (re-)construction. An increase in the accuracy of these parameters is expected as the result of this more systematic approach.

Bontekoe, Tj. R.↗

NASA NTRS1991

Image construction from the IRAS survey

IRAS survey data can be used successfully to produce images of extended objects. The major difficulties, i.e., nonuniform sampling, different response functions for each detector, and varying signal-to-noise levels for each detector for each scan, have been resolved. The results of three different image construction techniques are compared: coaddition, constrained least-squares, and maximum entropy. The maximum entropy result is superior. An image of the galaxy M51 with an average spatial resolution of 45 arcsecods, using 60 microns survey data is presented. This exceeds the telescope diffraction limit of about 1 minute of arc at this wavelength.

Bontekoe, T. R.↗

DOE OSTI2016

Fast and Efficient Stochastic Optimization for Analytic Continuation

In this analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM) as a more accessible variant of the stochastic optimization method introduced by Mishchenko et al. [Phys. Rev. B 62, 6317 (2000)], and we benchmark the resulting spectra with those obtained by the standard maximum entropy method for three representative test cases, including data taken from studies of the two-dimensional Hubbard model. Genearally, we find that our FESOM approach yields spectra similar to the maximum entropy results. In particular, while the maximum entropy method yields superior results when the quality of the data is strong, we find that FESOM is able to resolve fine structure with more detail when the quality of the data is poor. In addition, because of its stochastic nature, the method provides detailed information on the frequency-dependent uncertainty of the resulting spectra, while the maximum entropy method does so only for the spectral weight integrated over a finite frequency region. Therefore, we believe that this variant of the stochastic optimization approach provides a viable alternative to the routinely used maximum entropy method, especially for data of poor quality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Nonequilibrium statistical mechanics and optimal prediction of partially-observed complex systems

Abstract Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Probabilistic constitutive relationships for cyclic material strength models

A methodology is developed that provides a probabilistic treatment for the lifetime of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs.

Boyce, L.↗

NASA NTRS1989

Probabilistic analysis for fatigue strength degradation of materials

This report presents the results of the first year of a research program conducted for NASA-LeRC by the University of Texas at San Antonio. The research included development of methodology that provides a probabilistic treatment of lifetime prediction of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Linear elastic fracture mechanics is utilized in the latter model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs, RANDOM2, RANDOM3, and RANDOM4. These programs determine the random lifetime of an engine component, in mechanical load cycles, to reach a critical fatigue strength or crack size. The material considered was a cast nickel base superalloy, one typical of those used in the Space Shuttle Main Engine.

Royce, Lola↗

NASA NTRS1998

Solar Flare Physics

We have continued our previous efforts in studies of fourier imaging methods applied to hard X-ray flares. We have performed physical and theoretical analysis of rotating collimator grids submitted to GSFC(Goddard Space Flight Center) for the High Energy Solar Spectroscopic Imager (HESSI). We have produced simulation algorithms which are currently being used to test imaging software and hardware for HESSI. We have developed Maximum-Entropy, Maximum-Likelihood, and "CLEAN" methods for reconstructing HESSI images from count-rate profiles. This work is expected to continue through the launch of HESSI in July, 2000. Section 1 shows a poster presentation "Image Reconstruction from HESSI Photon Lists" at the Solar Physics Division Meeting, June 1998; Section 2 shows the text and viewgraphs prepared for "Imaging Simulations" at HESSI's Preliminary Design Review on July 30, 1998.

Schmahl, Edward J.↗

DOE OSTI2021

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1993

Energy transports by ocean and atmosphere based on an entropy extremum principle. I - Zonal averaged transports

The maximum entropy production principle suggested by Paltridge (1975) is applied to separating the satellite-determined required total transports into atmospheric and oceanic components. Instead of using the excessively restrictive equal energy dissipation hypothesis as a deterministic tool for separating transports between the atmosphere and ocean fluids, the satellite-inferred required 2D energy transports are imposed on Paltridge's energy balance model, which is then solved as a variational problem using the equal energy dissipation hypothesis only to provide an initial guess field. It is suggested that Southern Ocean transports are weaker than previously reported. It is argued that a maximum entropy production principle can serve as a governing rule on macroscale global climate, and, in conjunction with conventional satellite measurements of the net radiation balance, provides a means to decompose atmosphere and ocean transports from the total transport field.

Sohn, Byung-Ju↗

DOE OSTI2015

The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics

We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible correlation in the area of quantum phase transitions is a major motivation for this research. We extend a representation of the irreducible correlation from finite temperatures to absolute zero.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Estimation and uncertainty quantification for the output from quantum simulators

The problem of estimating certain distributions over {0, 1} d is considered here. The distribution represents a quantum system of d qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is adopted to reconstruct the distribution from exact moments or observed empirical moments. The Robbins Monro algorithm is used to solve the intractable maximum entropy problem, by constructing an unbiased estimator of the un-normalized target with a sequential Monte Carlo sampler at each iteration. In the case of empirical moments, this coincides with a maximum likelihood estimator. A Bayesian formulation is also considered in order to quantify uncertainty a posteriori. Several approaches are proposed in order to tackle this challenging problem, according to recently developed methodologies. In particular, unbiased estimators of the gradient of the log posterior are constructed and used within a provably convergent Langevin-based Markov chain Monte Carlo method. The methods are illustrated on classically simulated output from quantum simulators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments

Molecular extended thermodynamics of rarefied polyatomic gases is characterized by two hierarchies of equations for moments of a suitable distribution function in which the internal degrees of freedom of a molecule is taken into account. On the basis of physical relevance the truncation orders of the two hierarchies are proven to be not independent on each other, and the closure procedures based on the maximum entropy principle (MEP) and on the entropy principle (EP) are proven to be equivalent. The characteristic velocities of the emerging hyperbolic system of differential equations are compared to those obtained for monatomic gases and the lower bound estimate for the maximum equilibrium characteristic velocity established for monatomic gases (characterized by only one hierarchy for moments with truncation order of moments N) by Boillat and Ruggeri (1997) (λ{sub (N)}{sup E,max})/(c{sub 0}) ⩾√(6/5 (N−1/2 )),(c{sub 0}=√(5/3 k/m T)) is proven to hold also for rarefied polyatomic gases independently from the degrees of freedom of a molecule. -- Highlights: •Molecular extended thermodynamics of rarefied polyatomic gases is studied. •The relation between two hierarchies of equations for moments is derived. •The equivalence of maximum entropy principle and entropy principle is proven. •The characteristic velocities are compared to those of monatomic gases. •The lower bound of the maximum characteristic velocity is estimated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Reconstruction of Electron and Ion Distribution Functions in a Magnetotail Reconnection Diffusion Region

In the diffusion region of magnetotail reconnection, particle distributions are highly structured, exhibiting triangular shapes and multiple striations that deviate dramatically from the Maxwellian distribution. Fully kinetic simulations have been demonstrated to be capable of producing the essential structures of the observed distribution functions, yet are computationally not feasible for 3D global simulations. The fluid models used for large-scale simulations, on the other hand, do not have the kinetic physics necessary for describing reconnection accurately. Our study aims to bridge fully kinetic and fluid simulations by quantifying the information required to capture the non-Maxwellian features in the distributions underlying the closures used in the fluid code. Here, we compare the results of fully kinetic simulations with observed electron velocity distributions in a magnetotail reconnection diffusion region and use the maximum entropy model to reconstruct electron and ion distributions using various numbers of moments obtained from the simulation. Our results indicate that using only local moments, the maximum entropy model can reproduce many of the features of the distributions: (1) the electron outflow distribution with a tilted triangular structure is reproduced with 21 or more moments in agreement with Ng et al. and (2) counterstreaming distributions can be captured with the 35-moment model when the separation in velocity space between the populations is large.

58 GEOSCIENCES↗

NASA NTRS1990

High-resolution imaging of globular cluster cores

An approach based on the maximum entropy method aimed at increasing angular resolution to study globular cluster cores is presented. To perform the image restoration the Gull-Skilling (1989) MEMSYS-3 code for maximum entropy reconstruction of arbitrary data sets was used. This software was recently applied to restoration of ESO images of the R136 object in the core of the 30 Doradus nebula. It was demonstrated that the software made it possible to restore an image at subpixel spatial scales which facilitates the detection of very high-resolution structure in the restored image.

Weir, N.↗

NASA NTRS1972

On the first-excursion probability in stationary narrow-band random vibration. II.

The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.

Yang, J.-N.↗

NASA NTRS1995

Reverberation mapping by regularized linear inversion

Reverberation mapping of active galactic nucleus (AGN) emission-line regions requires the numerical deconvolution of two time series. We suggest the application of a new method, regularized linear inversion, to the solution of this problem. This method possesses many good features; it imposes no restrictions on the sign of the response function; it can provide clearly defined uncertainty estimates; it involves no guesswork about unmeasured data; it can give a clear indication of when the underlying convolution model is inadequate; and it is computationally very efficient. Using simulated data, we find the minimum S/N and length of the time series in order for this method to work satisfactorily. We also define guidelines for choosing the principal tunable parameter of the method and for interpreting the results. Finally, we reanalyze published data from the 1989 NGC 5548 campaign using this new method and compare the results to those previously obtained by maximum entropy analysis. For some lines we find good agreement, but for others, especially C III lambda(1909) and Si IV lambda(1400), we find significant differences. These can be attributed to the inability of the maximum entropy method to find negative values of the response function, but also illustrate the nonuniqueness of any deconvolution technique. We also find evidence that certain line light curves (e.g., C IV lambda(1549)) cannot be fully described by the simple linear convolution model.

Krolik, Julian H.↗

DOE OSTI2018

MULTI-PRED: A Software Module for Predictive Modeling of Coupled Multi-Physics Systems: User's Manual

This User’s Manual describes the code module MULTI-PRED, written in FORTRAN which implements the methodology for “predictive modeling of coupled multi-physics systems (PM-CMPS)” formulated by Cacuci (2014). This methodology fully takes into account the coupling terms between the systems but requires only the computational resources that would be needed to perform predictive modeling on each system separately. The PM-CMPS methodology uses the maximum entropy principle to construct an optimal approximation of the unknown a priori distribution based on a priori known mean values and uncertainties characterizing the experimental and computational parameters and results of interest responses, called for the multi-physics models under consideration. This “maximum entropy” a priori distribution is combined, using Bayes’ theorem, with the “likelihood” provided by the multi-physics simulation models to obtain a formal posterior distribution. Subsequently, the posterior distribution thus obtained is evaluated using the saddle-point method to obtain analytical expressions for the optimally predicted values for the multi-physics models parameters and responses along with corresponding reduced uncertainties. Noteworthy, the predictive modeling methodology for the coupled systems is constructed such that the systems can be considered sequentially rather than simultaneously, while preserving exactly the same results as if the systems were treated simultaneously. Consequently, very large coupled systems, which could perhaps exceed available computational resources if treated simultaneously, can be treated with the PM-CMPS methodology presented in this work sequentially and without any loss of generality or information, requiring just the resources that would be needed if the systems were treated sequentially. Three illustrative demonstration problems are also provided. The first problem presents the application of the PM-CMPS methodology to a simple particle diffusion problem which admits a closed-form analytical solution which facilitates a rapid understanding of this methodology and its predicted results. The second demonstration problem presents the application of the PM-CMPS methodology to the problem of inverse prediction, from detector responses in the presence of counting uncertainties, of the thickness of a homogeneous slab of material containing uniformly distributed gamma-emitting sources, for optically thin and thick slabs. This problem highlights the essential role played by the relative uncertainties (or, conversely, accuracies) of measured and computed responses. The third demonstration problem presents the application of the PM-CMPS methodology to the F-area cooling towers at the Savannah River National Lab. This problem demonstrates that the PM-CMPS methodology reduces the predicted response uncertainties not only at locations where measurements are available, but also at locations where measurements are not available.

97 MATHEMATICS AND COMPUTING↗