SEARCH · Engineering Papers

Results for “maximum entropy”

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 55 records · Page 3

All sources NASA NTRS DOE OSTI

DOE OSTI2015

Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1994

Beyond maximum entropy: Fractal Pixon-based image reconstruction

We have developed a new Bayesian image reconstruction method that has been shown to be superior to the best implementations of other competing methods, including Goodness-of-Fit methods such as Least-Squares fitting and Lucy-Richardson reconstruction, as well as Maximum Entropy (ME) methods such as those embodied in the MEMSYS algorithms. Our new method is based on the concept of the pixon, the fundamental, indivisible unit of picture information. Use of the pixon concept provides an improved image model, resulting in an image prior which is superior to that of standard ME. Our past work has shown how uniform information content pixons can be used to develop a 'Super-ME' method in which entropy is maximized exactly. Recently, however, we have developed a superior pixon basis for the image, the Fractal Pixon Basis (FPB). Unlike the Uniform Pixon Basis (UPB) of our 'Super-ME' method, the FPB basis is selected by employing fractal dimensional concepts to assess the inherent structure in the image. The Fractal Pixon Basis results in the best image reconstructions to date, superior to both UPB and the best ME reconstructions. In this paper, we review the theory of the UPB and FPB pixon and apply our methodology to the reconstruction of far-infrared imaging of the galaxy M51. The results of our reconstruction are compared to published reconstructions of the same data using the Lucy-Richardson algorithm, the Maximum Correlation Method developed at IPAC, and the MEMSYS ME algorithms. The results show that our reconstructed image has a spatial resolution a factor of two better than best previous methods (and a factor of 20 finer than the width of the point response function), and detects sources two orders of magnitude fainter than other methods.

Puetter, Richard C.↗

NASA NTRS2017

Multi-Group Maximum Entropy Model for Translational Non-Equilibrium

The aim of the current work is to describe a new model for flows in translational non- equilibrium. Starting from the statistical description of a gas proposed by Boltzmann, the model relies on a domain decomposition technique in velocity space. Using the maximum entropy principle, the logarithm of the distribution function in each velocity sub-domain (group) is expressed with a power series in molecular velocity. New governing equations are obtained using the method of weighted residuals by taking the velocity moments of the Boltzmann equation. The model is applied to a spatially homogeneous Boltzmann equation with a Bhatnagar-Gross-Krook1(BGK) model collision operator and the relaxation of an initial non-equilibrium distribution to a Maxwellian is studied using the model. In addition, numerical results obtained using the model for a 1D shock tube problem are also reported.

Entropy↗

DOE OSTI2024

Maximum Entropy Theory of Multiscale Coarse-Graining via Matching Thermodynamic Forces: Application to a Molecular Crystal (TATB)

The MSCG/FM (multiscale coarse-graining via force-matching) approach is an efficient supervised machine learning method to develop microscopically informed coarse-grained (CG) models. Here we present a theory based on the principle of maximum entropy (PME) enveloping the existing MSCG/FM approaches. This theory views the MSCG/FM method as a special case of matching the thermodynamic forces from the extended ensemble described by the set of thermodynamic (relevant) system coordinates. This set may include CG coordinates, the stress tensor, applied external fields, and so forth, and may be characterized by nonequilibrium conditions. Following the presentation of the theory, we discuss the consistent matching of both bonded and nonbonded interactions. The proposed PME formulation is used as a starting point to extend the MSCG/FM method to the constant strain ensemble, which together with the explicit matching of the bonded forces is better suited for coarse-graining anisotropic media at a submolecular resolution. The theory is demonstrated by performing the fine coarse-graining of crystalline 1,3,5-triamino-2,4,6-trinitrobenzene (TATB), a well-known insensitive molecular energetic material, which exhibits highly anisotropic mechanical properties.

1,3,5-triamino-2,4,6-trinitrobenzene↗

NASA NTRS1990

A homotopy algorithm for synthesizing robust controllers for flexible structures via the maximum entropy design equations

One well known deficiency of LQG compensators is that they do not guarantee any measure of robustness. This deficiency is especially highlighted when considering control design for complex systems such as flexible structures. There has thus been a need to generalize LQG theory to incorporate robustness constraints. Here we describe the maximum entropy approach to robust control design for flexible structures, a generalization of LQG theory, pioneered by Hyland, which has proved useful in practice. The design equations consist of a set of coupled Riccati and Lyapunov equations. A homotopy algorithm that is used to solve these design equations is presented.

Collins, Emmanuel G., Jr.↗

NASA NTRS2023

Using Regionalized Air Quality Model Performance and Bayesian Maximum Entropy Data Fusion to Map Global Surface Ozone Concentration and Associated Uncertainty

Estimates of ground-level ozone concentrations have been improved through data fusion of observations and atmospheric chemistry models. Our previous global ozone estimates for the Global Burden of Disease study corrected for bias uniformly across continents and then corrected near monitoring stations using the Bayesian Maximum Entropy (BME) framework for data fusion. Here, we use the Regionalized Air Quality Model Performance (RAMP) framework to correct model bias over a much larger spatial range than BME can, accounting for the spatial inhomogeneity of bias and nonlinearity as a function of modeled ozone. RAMP bias correction is applied to a composite of 9 global chemistry-climate models, based on the nearest set of monitors. These estimates are then fused with observations using BME, which matches observations at measurement stations, with the influence of observations declining with distance in space and time. We create global ozone maps for each year from 1990 to 2017 at fine spatial resolution. RAMP is shown to create unrealistic discontinuities due to the spatial clustering of ozone monitors, which we overcome by applying a weighting for RAMP based on the number of monitors nearby. Incorporating RAMP before BME has little effect on model performance near stations, but strongly increases R 2 by 0.15 at locations farther from stations, shown through a checkerboard cross-validation. Corrections to estimates differ based on location in space and time, confirming heterogeneity. We quantify the likelihood of exceeding selected ozone levels, finding that parts of the Middle East, India, and China are most likely to exceed 55 parts per billion (ppb) in 2017. About 96% of the global population was exposed to ozone levels above the World Health Organization guideline of 60 µg m −3 (30 ppb) in 2017. Our annual fine-resolution ozone estimates may be useful for several applications including epidemiology and assessments of impacts on health, agriculture, and ecosystems.

Ozone↗

DOE OSTI2018

Using the maximum entropy distribution to describe electrons in reconnecting current sheets

Particle distributions in weakly collisional environments such as the magnetosphere have been observed to show deviations from the Maxwellian distribution. These can often be reproduced in kinetic simulations, but fluid models, which are used in global simulations of the magnetosphere, do not necessarily capture any of this. We apply the maximum entropy fluid closure of Levermore, which leads to well posed moment equations, to reconstruct particle distributions from a kinetic simulation in a reconnection region. Our results show that without information other than the moments, the model can reproduce the general structure of the distributions but not all of the finer details. In conclusion, the advantages of the closure over the traditional Grad closure are also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

The Entropy Maximum in Scale-Invariant Processes with 1/f {sup α} Power Spectrum: the Effect of White Noise Anisotropy

Extreme fluctuations are simulated by a system of nonlinear stochastic equations describing the interacting phase transitions. Random 1/f {sup α} processes are formed under the action of anisotropic white noise with α-dependence of the power spectra on frequency and exponent α ranging from 0.7 to 1.7. It is shown that fluctuations with 1/f {sup α} power spectra in the studied range of α correspond to the entropy maximum, which indicates the stability of such processes at different values of exponent α.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Solvent effects determine the sign of the charges of maximum entropy and capacitance at silver electrodes

Fully harnessing electrochemical interfaces for reactions requires a detailed understanding of solvent effects in the electrochemical double layer. Predicting the significant impact of solvents on entropic and electronic properties of electrochemical interfaces has remained an open challenge of computational electrochemistry. Using molecular dynamics simulations of silver–water and silver–acetonitrile interfaces, we show that switching the solvent changes the signs for both the charge of maximum capacitance (CMC) and charge of maximum entropy (CME). Contrasting the capacitance and CME behavior of these two interfaces, we demonstrate that the preferred orientation of the solvent molecule and the corresponding charge density determine the sign of the CMC and CME and, hence, the qualitatively different charge asymmetry of the electrochemical interface.

Chemistry↗

DOE OSTI2025

Quantum maximum entropy closure for small flavor coherence

Quantum angular moment transport schemes are an important avenue toward describing neutrino flavor mixing phenomena in dense astrophysical environments such as supernovae and merging neutron stars. Successful implementation will require new closure relations that go beyond those used in classical transport. In this paper, we derive the first analytic expression for a quantum M1 closure, valid in the limit of small flavor coherence, based on the maximum entropy principle. We verify that the resulting closure relation has the appropriate limits and characteristic speeds in the diffusive and free-streaming regimes. We then use this new closure in a moment linear stability analysis to search for fast flavor instabilities in a binary neutron star merger simulation and find better results as compared with previously designed, ad hoc , semiclassical closures.

astrophysical & cosmological simulations↗

NASA NTRS2021

Mapping Yearly Fine Resolution Global Surface Ozone through the Bayesian Maximum Entropy Data Fusion of Observations and Model Output for 1990–2017

Estimates of ground-level ozone concentrations are necessary to determine the human health burden of ozone. To support the Global Burden of Disease Study, we produce yearly fine resolution global surface ozone estimates from 1990 to 2017 through a data fusion of observations and models. As ozone observations are sparse in many populated regions, we use a novel combination of the M3Fusion and Bayesian Maximum Entropy (BME) methods. With M3Fusion, we create a multi-model composite by bias-correcting and weighting nine global atmospheric chemistry models based on their ability to predict observations (8,834 sites globally)in each region and year. BME is then used to integrate observations, such that estimates match observations at each monitoring site with the observational influence decreasing smoothly across space and time until the output matches the multi-model composite. After estimating at 0.5° resolution using BME, we add fine spatial detail from an additional model, yielding estimates at 0.1° resolution. Observed ozone is predicted more accurately (R2=0.81 at test point, 0.63 at 0.1°,0.62 at 0.5°) than the multi-model mean (R2=0.28 at 0.5°). Global ozone exposure is estimated to be increasing, driven by highly populated regions of Asia and Africa, despite decreases in the United States and Russia.

environmental modeling↗

NASA NTRS1990

Test images for the maximum entropy image restoration method

One of the major activities of any experimentalist is data analysis and reduction. In solar physics, remote observations are made of the sun in a variety of wavelengths and circumstances. In no case is the data collected free from the influence of the design and operation of the data gathering instrument as well as the ever present problem of noise. The presence of significant noise invalidates the simple inversion procedure regardless of the range of known correlation functions. The Maximum Entropy Method (MEM) attempts to perform this inversion by making minimal assumptions about the data. To provide a means of testing the MEM and characterizing its sensitivity to noise, choice of point spread function, type of data, etc., one would like to have test images of known characteristics that can represent the type of data being analyzed. A means of reconstructing these images is presented.

Mackey, James E.↗

DOE OSTI2023

A Modified Maximum Entropy Inverse Reinforcement Learning Approach for Microgrid Energy Scheduling

Increasing popularity of integrating distributed energy resources (DERs) into the power system brings a challenge to optimize the microgrid dispatch policy. The reinforcement learning methods suffer from a long-time problem with the theoretical assumption of the objective/reward function for the microgrid system. Although the traditional inverse reinforcement learning (IRL) approaches can solve this problem to some extent, they encounter a limitation of complex computations for state visitation frequency in the large and continuous state space. To alleviate this limitation, we propose a modified maximum entropy IRL (MMIRL) method to extract the reward function from the expert demonstrations for solving the microgrid energy scheduling problem. The proposed MMIRL algorithm is promising in recovering the reward function and learning the dispatch policy compared to conventional approaches. Case studies are performed in an energy arbitrage problem and a microgrid system with DERs. Results substantiate that the proposed MMIRL approach can learn the dispatch policy with more than 99% efficiency and outperforms other comparative methods.

artificial intelligence, reinforcement learning, m↗

DOE OSTI2012

Investigation of a high spatial resolution method based on polar coordinate maximum entropy method for analyzing electron density fluctuation data measured by laser phase contrast

Laser phase contrast is a powerful diagnostic method to determine the spatial distribution of electron density fluctuations in magnetically confined plasmas, although its applicability depends on magnetic field configurations. The spatial resolution of fluctuations is linked with the resolution of the propagation direction that is derived from the two-dimensional spectral analysis of the wavenumber for the fluctuations. The method was applied to fluctuation measurements in a compact helical system. In order to improve the resolution of the propagation direction with a relatively small number of data points, the maximum entropy method with polar coordinates was employed. A spatial resolution of the order of 1 cm was obtained, which is satisfactory in a plasma with a 20 cm minor radius.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.

Eigenstate thermalization↗

DOE OSTI2011

Probing local structure in the yellow phosphor LaSr[subscript 2]AlO[subscript 5]:Ce[superscript 3+], by the maximum entropy method and pair distribution function analysis

The compound LaSr{sub 2}AlO{sub 5} was recently introduced as a competitive Ce{sup 3+} host material for blue-pumped yellow phosphors for use in white light emitting diodes. A crucial feature of the crystal structure of LaSr{sub 2}AlO{sub 5} is that La, which is the host site for Ce{sup 3+}, is located in the 8h positions of the I4/mcm crystal structure, a site equally shared with Sr. While the average crystal structure of LaSr{sub 2}AlO{sub 5} as revealed by Rietveld analysis of laboratory and synchrotron X-ray diffraction data suggests nothing untoward, maximum entropy method analysis of the synchrotron X-ray data reveals the existence of conspicuous non-sphericity of the electron density. Pair distribution function analysis of the data suggests that despite their occupying the same crystallographic site, La and Sr possess distinct coordination environments, and the environment around La is more compact and regular than the environment suggested by the Rietveld refinement of the average structure. The absorption and emission from Ce{sup 3+} centers is controlled by the local coordination and symmetry, and the use of powerful new tools in unraveling details of these strengthens the rational search for new phosphors for solid state white lighting.

36 MATERIALS SCIENCE↗

NASA NTRS1984

On the maximum-entropy/autoregressive modeling of time series

The autoregressive (AR) model of a random process is interpreted in the light of the Prony's relation which relates a complex conjugate pair of poles of the AR process in the z-plane (or the z domain) on the one hand, to the complex frequency of one complex harmonic function in the time domain on the other. Thus the AR model of a time series is one that models the time series as a linear combination of complex harmonic functions, which include pure sinusoids and real exponentials as special cases. An AR model is completely determined by its z-domain pole configuration. The maximum-entropy/autogressive (ME/AR) spectrum, defined on the unit circle of the z-plane (or the frequency domain), is nothing but a convenient, but ambiguous visual representation. It is asserted that the position and shape of a spectral peak is determined by the corresponding complex frequency, and the height of the spectral peak contains little information about the complex amplitude of the complex harmonic functions.

Chao, B. F.↗

NASA NTRS1989

Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

Hsia, Wei Shen↗