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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

MENT-Flow: maximum-entropy phase space tomography using normalizing flows

Generative models can be trained to reproduce low-dimensional projections of high-dimensional phase space distributions. Normalizing flows are generative models that parameterize invertible transformations, allowing exact probability density evaluation and sampling. Consequently, flows are unbiased entropy estimators and could be used to solve the high-dimensional maximum-entropy tomography (MENT) problem. In this work, we evaluate a flow-based MENT solver (MENT-Flow) against exact maximum-entropy solutions and Minerbo's iterative MENT algorithm in two dimensions.

Hoover, Austin↗
NASA NTRS1991

Maximum entropy method applied to deblurring images on a MasPar MP-1 computer

A statistical inference method based on the principle of maximum entropy is developed for the purpose of enhancing and restoring satellite images. The proposed maximum entropy image restoration method is shown to overcome the difficulties associated with image restoration and provide the smoothest and most appropriate solution consistent with the measured data. An implementation of the method on the MP-1 computer is described, and results of tests on simulated data are presented.

Bonavito, N. L.↗
DOE OSTI2012

A Maximum-Entropy approach for accurate document annotation in the biomedical domain

The increasing number of scientific literature on the Web and the absence of efficient tools used for classifying and searching the documents are the two most important factors that influence the speed of the search and the quality of the results. Previous studies have shown that the usage of ontologies makes it possible to process document and query information at the semantic level, which greatly improves the search for the relevant information and makes one step further towards the Semantic Web. A fundamental step in these approaches is the annotation of documents with ontology concepts, which can also be seen as a classification task. In this paper we address this issue for the biomedical domain and present a new automated and robust method, based on a Maximum Entropy approach, for annotating biomedical literature documents with terms from the Medical Subject Headings (MeSH). The experimental evaluation shows that the suggested Maximum Entropy approach for annotating biomedical documents with MeSH terms is highly accurate, robust to the ambiguity of terms, and can provide very good performance even when a very small number of training documents is used. More precisely, we show that the proposed algorithm obtained an average F-measure of 92.4% (precision 99.41%, recall 86.77%) for the full range of the explored terms (4,078 MeSH terms), and that the algorithm’s performance is resilient to terms’ ambiguity, achieving an average F-measure of 92.42% (precision 99.32%, recall 86.87%) in the explored MeSH terms which were found to be ambiguous according to the Unified Medical Language System (UMLS) thesaurus. Finally, we compared the results of the suggested methodology with a Naive Bayes and a Decision Trees classification approach, and we show that the Maximum Entropy based approach performed with higher F-Measure in both ambiguous and monosemous MeSH terms.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
NASA NTRS1979

A dual method for maximum entropy restoration

A simple iterative dual algorithm for maximum entropy image restoration is presented. The dual algorithm involves fewer parameters than conventional minimization in the image space. Minicomputer test results for Fourier synthesis with inadequate phantom data are given.

Smith, C. B.↗
DOE OSTI2014

Possible dynamical explanations for Paltridge's principle of maximum entropy production

Throughout the history of non-equilibrium thermodynamics a number of theories have been proposed in which complex, far from equilibrium flow systems are hypothesised to reach a steady state that maximises some quantity. Perhaps the most celebrated is Paltridge's principle of maximum entropy production for the horizontal heat flux in Earth's atmosphere, for which there is some empirical support. There have been a number of attempts to derive such a principle from maximum entropy considerations. However, we currently lack a more mechanistic explanation of how any particular system might self-organise into a state that maximises some quantity. This is in contrast to equilibrium thermodynamics, in which models such as the Ising model have been a great help in understanding the relationship between the predictions of MaxEnt and the dynamics of physical systems. In this paper we show that, unlike in the equilibrium case, Paltridge-type maximisation in non-equilibrium systems cannot be achieved by a simple dynamical feedback mechanism. Nevertheless, we propose several possible mechanisms by which maximisation could occur. Showing that these occur in any real system is a task for future work. The possibilities presented here may not be the only ones. We hope that by presenting them we can provoke further discussion about the possible dynamical mechanisms behind extremum principles for non-equilibrium systems, and their relationship to predictions obtained through MaxEnt.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

𝑁-dimensional maximum-entropy tomography via particle sampling

We propose a modified maximum-entropy (MENT) algorithm for six-dimensional phase space tomography. The algorithm uses particle sampling and low-dimensional density estimation to approximate large sets of high-dimensional integrals in the original MENT formulation. We implement this approach using Markov Chain Monte Carlo (MCMC) sampling techniques and demonstrate convergence of six-dimensional MENT on both synthetic and measured data.

Hoover, Austin [Oak Ridge National Laboratory (ORN↗
DOE OSTI2022

Investigation of Molecular Diffusion at Block Copolymer Thin Films Using Maximum Entropy Method-Based Fluorescence Correlation Spectroscopy and Single Molecule Tracking

Fluorescence correlation spectroscopy (FCS) has been widely used to investigate molecular diffusion behavior in various samples. The use of the maximum entropy method (MEM) for FCS data analysis provides a unique means to determine multiple distinct diffusion coefficients without a priori assumption of their number. Comparison of the MEM-based FCS method (MEM-FCS) with another method will reveal its utility and advantage as an analytical tool to investigate diffusion dynamics. Herein, we measured diffusion of fluorescent probes doped into nanostructured thin films using MEM-FCS, and validated the results with single molecule tracking (SMT) data. The efficacy of the MEM code employed was first demonstrated by analyzing simulated FCS data for systems incorporating one and two diffusion modes with broadly distributed diffusion coefficients. The MEM analysis accurately afforded the number of distinct diffusion modes and their mean diffusion coefficients. These results contrasted with those obtained by fitting the simulated data to conventional two-component and anomalous diffusion models, which yielded inaccurate estimates of the diffusion coefficients. Subsequently, the MEM analysis was applied to FCS data acquired from hydrophilic dye molecules incorporated into microphase-separated polystyrene-block-poly(ethylene oxide) (PS-b-PEO) thin films characterized under a water-saturated nitrogen atmosphere. The MEM analysis revealed distinct fast and slow diffusion components attributable to molecules diffusing on the film surface and inside the film, respectively. SMT studies of the same materials yielded trajectories for mobile molecules that appear to follow the curved PEO microdomains. Diffusion coefficients obtained from the SMT data were consistent with those obtained for the slow diffusion component detected by MEM-FCS. Furthermore, these results highlight the utility of MEM-FCS and SMT for gaining complementary information on molecular diffusion processes in heterogeneous material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A maximum entropy principle for inferring the distribution of 3D plasmoids

The principle of maximum entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive MHD is applicable and large numbers of plasmoids are produced. The analysis is undertaken for the 3D case, with mass, total flux, and velocity serving as the variables of interest, on account of their physical and observational relevance. The distribution functions for the mass, width, total flux, and helicity exhibit a power-law behavior with exponents of -4/3, -2, -3, and -2, respectively, for small values, whilst all of them display an exponential falloff for large values. In contrast, the velocity distribution, as a function of v=|v|, is shown to be flat for v→0, and becomes a power law with an exponent of -7/3 for v→∞. Most of these results are nearly independent of the free parameters involved in this specific problem. In conclusion, a preliminary comparison of our results with the observational evidence is presented, and some of the ensuing space and astrophysical implications are briefly discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Modelling bivariate extreme precipitation distribution for data-scarce regions using Gumbel-Hougaard copula with maximum entropy estimation

A new method of parameter estimation in data scarce regions is valuable for bivariate hydrological extreme frequency analysis. Here, this paper proposes a new method of parameter estimation (maximum entropy estimation, MEE) for both Gumbel and Gumbel–Hougaard copula in situations when insufficient data are available. MEE requires only the lower and upper bounds of two hydrological variables. To test our new method, two experiments to model the joint distribution of the maximum daily precipitation at two pairs of stations on the tributaries of Heihe and Jinghe River, respectively, were performed and compared with the method of moments, correlation index estimation, and maximum likelihood estimation, which require a large amount of data. Both experiments show that for the Ye Niugou and Qilian stations, the performance of MEE is nearly identical to those of the conventional methods. For the Xifeng and Huanxian stations, MEE can capture information indicating that the maximum daily precipitation at the Xifeng and Huanxian stations has an upper tail dependence, whereas the results generated by correlation index estimation and maximum likelihood estimation are unreasonable. Moreover, MEE is proved tobe generally reliable and robust by many simulations under three different situations. TheGumbel–Hougaard copula with MEE can also be applied to the bivariate frequency analysis ofother extreme events in data-scarce regions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Integrating Maximum Entropy Production Theory and Machine Learning to Improve Global Evapotranspiration Modeling

Accurate estimation of terrestrial evapotranspiration (ET) is vital for understanding global water and energy cycles. However, current global ET estimations are not well constrained. This study introduces an integrated framework combining the Maximum Entropy Production (MEP) theory with Random Forest (RF) model to improve global ET estimation. Specifically, in contrast to direct ET estimation by the RF model, the integrated framework (MEP‐RF) trains to predict error of MEP‐simulated ET. MEP‐RF outperforms RF in spatiotemporal extrapolation. Attribution analysis with in situ observations reveals that the inputs of MEP are the most critical variables for the ET process, including net radiation, vegetated area, soil moisture, and surface temperature. We further drive MEP‐RF with global reanalysis and satellite data sets of these four inputs, yielding a global mean terrestrial ET of 548 mm/year, with 77% attributed to transpiration. The global ET increased at a rate of 0.85 mm/year per year during 2003–2021, primarily due to vegetation greening rather than rising temperature, while decreasing soil moisture led to decreasing regional ET. The integrated framework provides a novel approach for the estimation of global ET without the need for hard‐to‐obtain and thus uncertain inputs, such as wind speed, surface roughness, aerodynamic and canopy stomatal resistance. Therefore, MEP‐RF offers an independent method on existing global ET products. It represents a promising physically based approach that can be incorporated into Earth System Models to enhance water and energy cycle simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approach

We study the continuity of an abstract generalization of the maximum-entropy inference—a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function on the convex body. Using convex geometry we prove, amongst others, the existence of discontinuities of the maximizer at limits of extremal points not being extremal points themselves and apply the result to quantum correlations. Further, we use numerical range methods in the case of quantum inference which refers to two observables. One result is a complete characterization of points of discontinuity for 3 × 3 matrices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Halo-independence with quantified maximum entropy at DAMA/LIBRA

Using the DAMA/LIBRA anomaly as an example, we formalise the notion of halo-independence in the context of Bayesian statistics and quantified maximum entropy. We consider an infinite set of possible profiles, weighted by an entropic prior and constrained by a likelihood describing noisy measurements of modulated moments by DAMA/LIBRA. Assuming an isotropic dark matter (DM) profile in the galactic rest frame, we find the most plausible DM profiles and predictions for unmodulated signal rates at DAMA/LIBRA. The entropic prior contains an a priori unknown regularisation factor, β, that describes the strength of our conviction that the profile is approximately Maxwellian. By varying β, we smoothly interpolate between a halo-independent and a halo-dependent analysis, thus exploring the impact of prior information about the DM profile.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Estimation of Evapotranspiration of Amazon Rainforest Using the Maximum Entropy Production Method

Energy budget of Amazonian forests has a large influence on regional and global climate, but relevant data are scarce. A novel energy partition method based on the maximum entropy production (MEP) theory is applied to simulate evapotranspiration in Amazonia. Using site-level eddy flux data, the MEP method shows high skill at the hourly, daily, and monthly scales. Consistent performance under different levels of land surface dryness is revealed, hinting that drought signal is appropriately resolved. The site-level MEP-based estimates outperform the estimates of the Moderate Resolution Imaging Spectroradiometer evapotranspiration product, which is commonly used for large-scale assessments. At the Amazon basin scale, the two series yield similar averages but exhibit spatial differences. The parameter parsimony and demonstrated skill of the MEP method make it an attractive approach for environments with diverse strategies of water flux control.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2011

Integrating Correlated Bayesian Networks Using Maximum Entropy

We consider the problem of generating a joint distribution for a pair of Bayesian networks that preserves the multivariate marginal distribution of each network and satisfies prescribed correlation between pairs of nodes taken from both networks. We derive the maximum entropy distribution for any pair of multivariate random vectors and prescribed correlations and demonstrate numerical results for an example integration of Bayesian networks.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2019

Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”

We welcome the opportunity to correct the misunderstandings and misinterpretations contained in Yano’s comment that led him to incorrectly state that Wu and McFarquhar misunderstood the maximum entropy (MaxEnt) principle. As correctly stated by Yano, the principle itself does not suffer from the problem of a lack of invariance. But, as restated in this reply and in Wu and McFarquhar, the commonly used Shannon–Gibbs entropy does suffer from a lack of invariance for coordinate transform when applied in continuous cases, and this problem is resolved by the use of the relative entropy. Further, it is restated that the Wu and McFarquhar derivation of the PSD form using MaxEnt is more general than the formulation by Yano and allows more constraints with any functional relations to be applied. The derivation of Yano is nothing new but the representation of PSDs in other variables.

54 ENVIRONMENTAL SCIENCES↗
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 methods, including Goodness-of-Fit (e.g. Least-Squares and Lucy-Richardson) and Maximum Entropy (ME). 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.

Puetter, R. C.↗