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Results for “Diffusion maps”

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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Enabling probabilistic learning on manifolds through double diffusion maps

Here, we present a generative learning framework for probabilistic sampling that extends Probabilistic Learning on Manifolds (PLoM), which is designed to generate statistically consistent realizations of a random vector in a finite-dimensional Euclidean space, informed by a (representative) set of observations. In its original form, PLoM constructs a reduced-order probabilistic model by combining three main components: (a) kernel density estimation to approximate the underlying probability measure, (b) Diffusion Maps to characterize the manifold of the data, and (c) a reduced-order Itô Stochastic Differential Equation (ISDE) to sample from the learned distribution. However, its sampling dynamics are posed in the ambient space and the retained number of reduced coordinates is chosen by projection-reconstruction error. In practice, this often (i) requires more coordinates than the data’s intrinsic dimension to achieve stable sampling and (ii) lacks a smooth, basis-independent lifting back to the data domain; moreover, standard Diffusion Maps emphasize harmonic eigenfunctions and can miss non-harmonic latent structure. We address these limitations by decoupling geometry learning from sampling: a first Diffusion Maps pass identifies non-harmonic coordinates on which we formulate a full-order ISDE directly in the latent space, while Double Diffusion Maps captures multiscale geometric features and Geometric Harmonics (GH) learns a smooth lifting map to the ambient variables that is independent of the particular diffusion basis. This hybrid design preserves the system’s dynamical richness with a compact geometric representation and enables principled out-of-sample inference. The effectiveness and robustness of the proposed method are illustrated through two numerical studies: one based on data generated from two-dimensional Hermite polynomial functions and another based on high-fidelity simulations of a detonation wave in a reactive flow.

Double diffusion maps↗
NASA NTRS1991

The detection of X-rays from the hot interstellar medium of the Large Magellanic Cloud

A comprehensive reanalysis is presented of the Einstein IPC data base on the LMC, and a number of new algorithms are used to improve the reliability of the point source detection in this crowded region and to produce the first large-scale map of diffuse emission free from the effects of solar scattered X-rays and cosmic-ray particles. Algorithms described in detail include a technique to decontaminate fields containing solar scattered flux, a mechanism for obtaining a spectrum-weighted vignetting function, and a source excision and smoothing algorithm which results in a diffuse map of uniform statistical quality. A catalog of discrete X-rays sources in the direction of the LMC is presented which contains 33 new sources and eliminates a number of spurious and/or marginal directions from previous lists. A possible detection of the long-sought shadowing effect on the cosmic X-ray background produced by cold LMC gas is reported.

Wang, Q.↗
NASA NTRS2004

EGRET Diffuse Gamma Ray Maps Between 30 MeV and 10 GeV

This paper presents all-sky maps of diffuse gamma radiation in various energy ranges between 30 MeV and 10 GeV, based on data collected by the EGRET instrument on the Compton Gamma Ray Observatory. Although the maps can be used for a variety of applications, the immediate goal is the generation of diffuse gamma-ray maps which can be used as a diffuse background/foreground for point source analysis of the data to be obtained from new high-energy gamma-ray missions like GLAST and AGILE. To generate the diffuse gamma maps from the raw EGRET maps, the point sources in the Third EGRET Catalog were subtracted out using the appropriate point spread function for each energy range. After that, smoothing was performed to minimize the effects of photon statistical noise. A smoothing length of 1deg was used for the Galactic plane maps. For the all-sky maps, a procedure was used which resulted in a smoothing length roughly equivalent to 4deg. The result of this work is 16 maps of different energy intervals for [b]less than or equal to 20deg, and 32 all-sky maps, 16 in equatorial coordinates (J2000) and 16 in Galactic coordinates.

Cillis, A. N.↗
NASA NTRS2004

EGRET Diffuse Gamma Ray Maps Between 30 MeV and 10 GeV

This paper presents all-sky maps of diffuse gamma radiation in various energy ranges between 30 MeV and 10 GeV, based on data collected by the EGRET instrument on the Compton Gamma Ray Observatory. Although the maps can be used for a variety of applications. the immediate goal is the generation of diffuse gamma-ray maps which can be used as a diffuse background/foreground for point source analysis of the data to be obtained from new high-energy gamma-ray missions like GLAST and AGILE. To generate the diffuse gamma maps from the raw EGRET maps, the point sources in the Third EGRET Catalog were subtracted out using the appropriate point spread function for each energy range. After that, smoothing was performed to minimize the effects of photon statistical noise. A smoothing length of 1 deg vas used for the Galactic plane maps. For the all-sky maps, a procedure was used which resulted in a smoothing length roughly equivalent to 4 deg. The result of this work is 16 maps of different energy intervals for absolute value of b < or equal to 20 deg, and 32 all-sky maps, 16 in equatorial coordinates (J2000) and 16 in Galactic coordinates.

Cillis, A, N.↗
DOE OSTI2025

Latent diffusion can map beam loss to two-dimensional phase-space projections

Beam loss monitors (BLMs) and beam current monitors (BCMs) are ubiquitous at particle accelerators around the world. These simple devices provide noninvasive high-level beam measurements but give no insight into the detailed 6D (𝑥,𝑦,𝑧,𝑝 𝑥 ,𝑝 𝑦 ,𝑝 𝑧 ) beam phase-space distributions or dynamics. We show that generative conditional latent diffusion models can learn intricate patterns to solve the extreme inverse problem of mapping waveforms of tens of BLMs or BCMs along an accelerator to detailed 2D projections of a charged particle beam’s 6D phase-space density. This transformational method can be used at any particle accelerator to transform simple noninvasive devices into detailed beam phase-space diagnostics. We demonstrate this concept via multiparticle simulations of the high-intensity beam in the kilometer-long Los Alamos Neutron Science Center linear proton accelerator.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
DOE OSTI2024

Transient anisotropic kernel for probabilistic learning on manifolds

PLoM (Probabilistic Learning on Manifolds) is a method introduced in 2016 for handling small training datasets by projecting an Itô equation from a stochastic dissipative Hamiltonian dynamical system, acting as the MCMC generator, for which the KDE-estimated probability measure with the training dataset is the invariant measure. PLoM performs a projection on a reduced-order vector basis related to the training dataset, using the diffusion maps (DMAPS) basis constructed with a time-independent isotropic kernel. In this paper, we propose a new ISDE projection vector basis built from a transient anisotropic kernel, providing an alternative to the DMAPS basis to improve statistical surrogates for stochastic manifolds with heterogeneous data. The construction ensures that for times near the initial time, the DMAPS basis coincides with the transient basis. For larger times, the differences between the two bases are characterized by the angle of their spanned vector subspaces. The optimal instant yielding the optimal transient basis is determined using an estimation of mutual information from Information Theory, which is normalized by the entropy estimation to account for the effects of the number of realizations used in the estimations. Consequently, this new vector basis better represents statistical dependencies in the learned probability measure for any dimension. Three applications with varying levels of statistical complexity and data heterogeneity validate the proposed theory, showing that the transient anisotropic kernel improves the learned probability measure.

Diffusion maps↗
NASA NTRS1982

The soft X-ray diffuse background

Maps of the diffuse X-ray background intensity covering essentially the entire sky with approx. 7 deg spatial resolution are presented for seven energy bands. The data were obtained on a series of ten sounding rocket flights conducted over a seven-year period. The different nature of the spatial distributions in different bands implies at least three distinct origins for the diffuse X-rays, none of which is well-understood. At energies or approx. 2000 eV, an isotropic and presumably extraglalactic 500 and 1000 eV, an origin which is at least partially galactic seems called for. At energies 284 eV, the observed intensity is anticorrelated with neutral hydrogen column density, but we find it unlikely that this anticorrelation is simply due to absorption of an extragalactic or halo source.

Mccammon, D.↗
NASA NTRS1983

The soft X-ray diffuse background

Maps of the diffuse X-ray background intensity covering essentially the entire sky with approximately 7 deg spatial resolution are presented for seven energy bands. The data were obtained on a series of ten sounding rocket flights conducted over a seven-year period. The different nature of the spatial distributions in different bands implies at least three distinct origins for the diffuse X-rays, none of which is well-understood. At energies of approximately 2000 eV, an isotropic and presumably extragalactic 500 and 1000 eV, an origin which is at least partially galactic seems called for. At energies 284 eV, the observed intensity is anticorrelated with neutral hydrogen column density, but we find it unlikely that this anticorrelation is simply due to absorption of an extragalactic or halo source. Previously announced in STAR as N83-20892

Mccammon, D.↗
DOE OSTI2025

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their “space” and “time”) as well as their effective parameters are all emergent , i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the “space,” the “time” and the “parameter” axes of a tensor. Once the data become organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative examples are based (i) on a simple advection–diffusion model; (ii) on a previously developed vertex-plus-signaling model of Drosophila embryonic development; and (iii) on two complex dynamic network models (one neuronal and one coupled oscillator model) for which no obvious smooth embedding geometry is known a priori. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.

generative models↗
DOE OSTI2024

Revealing the hidden structure of disordered materials by parameterizing their local structural manifold

Abstract Durable interest in developing a framework for the detailed structure of glassy materials has produced numerous structural descriptors that trade off between general applicability and interpretability. However, none approach the combination of simplicity and wide-ranging predictive power of the lattice-grain-defect framework for crystalline materials. Working from the hypothesis that the local atomic environments of a glassy material are constrained by enthalpy minimization to a low-dimensional manifold in atomic coordinate space, we develop a generalized distance function, the Gaussian Integral Inner Product (GIIP) distance, in connection with agglomerative clustering and diffusion maps, to parameterize that manifold. Applying this approach to a two-dimensional model crystal and a three-dimensional binary model metallic glass results in parameters interpretable as coordination number, composition, volumetric strain, and local symmetry. In particular, we show that a more slowly quenched glass has a higher degree of local tetrahedral symmetry at the expense of cyclic symmetry. While these descriptors require post-hoc interpretation, they minimize bias rooted in crystalline materials science and illuminate a range of structural trends that might otherwise be missed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Active learning of ternary alloy structures and energies

Abstract Machine learning models with uncertainty quantification have recently emerged as attractive tools to accelerate the navigation of catalyst design spaces in a data-efficient manner. Here, we combine active learning with a dropout graph convolutional network (dGCN) as a surrogate model to explore the complex materials space of high-entropy alloys (HEAs). We train the dGCN on the formation energies of disordered binary alloy structures in the Pd-Pt-Sn ternary alloy system and improve predictions on ternary structures by performing reduced optimization of the formation free energy, the target property that determines HEA stability, over ensembles of ternary structures constructed based on two coordinate systems: (a) a physics-informed ternary composition space, and (b) data-driven coordinates discovered by the Diffusion Maps manifold learning scheme. Both reduced optimization techniques improve predictions of the formation free energy in the ternary alloy space with a significantly reduced number of DFT calculations compared to a high-fidelity model. The physics-based scheme converges to the target property in a manner akin to a depth-first strategy, whereas the data-driven scheme appears more akin to a breadth-first approach. Both sampling schemes, coupled with our acquisition function, successfully exploit a database of DFT-calculated binary alloy structures and energies, augmented with a relatively small number of ternary alloy calculations, to identify stable ternary HEA compositions and structures. This generalized framework can be extended to incorporate more complex bulk and surface structural motifs, and the results demonstrate that significant dimensionality reduction is possible in thermodynamic sampling problems when suitable active learning schemes are employed.

Chemistry↗
DOE OSTI2024

Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. Additionally, we identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2012

New Measurements of the Cosmic Infrared Background Fluctuations in Deep SpitzerllRAC Survey Data and their Cosmological Implications

We extend the previous measurements of CIB fluctuations to angular scales of less than or equal to 1 degree new data obtained in the course of the 2,000+ hour Spitzer Extended Deep Survey. Two fields with completed observations of approximately equal to 12 hr/pixel are analyzed for source-subtracted CIB fluctuations at 3.6 and 4.5 micrometers. The fields, EGS and UDS, cover a total area of approximately 0.25 deg and lie at high Galactic and Ecliptic latitudes, thus minimizing cirrus and zodiacal light contributions to the fluctuations. The observations have been conducted at 3 distinct epochs separated by about 6 months. As in our previous studies, the fields were assembled using the self-calibration method which is uniquely suitable for probing faint diffuse backgrounds. The assembled fields were cleaned off the bright sources down to the low shot noise levels corresponding to AB mag approximately equal to 25, Fourier-transformed and their power spectra evaluated. The noise was estimated from the time-differenced data and subtracted from the signal isolating the fluctuations remaining above the noise levels. The power spectra of the source-subtracted fields remain identical (within the observational uncertainties) for the three epochs of observations indicating that zodiacal light contributes negligibly to the fluctuations. By comparing to the measurements for the same regions at 8 micrometers we demonstrate that Galactic cirrus cannot account for the levels of the fluctuations either. The signal appears isotropically distributed on the sky as required by its origin in the CIB fluctuations. This measurement thus extends our earlier results to the important range of sub-degree scales. We find that the CIB fluctuations continue to diverge to more than 10 times those of known galaxy populations on angular scales out to less than or equal to 1 degree. The low shot noise levels remaining in the diffuse maps indicate that the large scale fluctuations arise from spatial clustering of faint sources well within the confusion noise. The spatial spectrum of these fluctuations is in reasonable agreement with simple fitting assuming that they originate in early populations spatially distributed according to the standard cosmological model (ACDM) at epochs coinciding with the first stars era. The alternative to this identification would require a new population never observed before, nor expected on theoretical grounds, but if true this would represent an important discovery in its own right.

Kashlinsky, A.↗
NASA NTRS1984

HEAO-1 Diffuse Soft X-ray Sky Maps

Maps of the diffuse X-ray background intensity are presented, spanning four energy intervals. The lowest energy interval (0.18 to 0.56 keV) is dominated by local emission, while the next two intervals (0.56 to 1.0 keV and 1.0 to 1.4 keV) reveal more distant and more sharply defined structures. Enlarged maps of several of these structures are presented, including the North Polar Spur, the Galactic Center region and the Eridanus Loop.

Nousek, J. A.↗
NASA NTRS2016

Solar Wind Charge Exchange Contribution To The ROSAT Sky Survey Maps

DXL (Diffuse X-ray emission from the Local Galaxy) is a sounding rocket mission designed to estimate the contribution of solar wind charge eXchange (SWCX) to the diffuse X-ray background and to help determine the properties of the Local Hot Bubble. The detectors are large area thin-window proportional counters with a spectral response that is similar to that of the PSPC (Position Sensitive Proportional Counters) used in the ROSAT All Sky Survey (RASS). A direct comparison of DXL and RASS data for the same part of the sky viewed from quite different vantage points in the solar system, and the assumption of approximate isotropy for the solar wind, allowed us to quantify the SWCX contribution to all six RASS bands (R1-R7, excluding R3). We find that the SWCX contribution at l = 140 degrees, b = 0 degrees, where the DXL path crosses the Galactic plane, is 33 percent plus or minus 6 percent (statistical) plus or minus 12 percent (systematic) for R1, 44 percent plus or minus 6 percent plus or minus 5 percent for R2, 18 percent plus or minus 12 percent plus or minus 11 percent for R4, 14 percent plus or minus 11 percent plus or minus 9 percent for R5, and negligible for the R6 and R7 bands. Reliable models for the distribution of neutral H and He in the solar system permit estimation of the contribution of interplanetary SWCX emission over the the whole sky and correction of the RASS maps. We find that the average SWCX contribution in the whole sky is 26 percent plus or minus 6 percent plus or minus 13 percent for R1, 30 percent plus or minus 4 percent plus or minus 4 percent for R2, 8 percent plus or minus 5 percent plus or minus 5 percent for R4, 6 percent plus or minus 4 percent plus or minus 4 percent for R5, and negligible for R6 and R7.

sxcx↗
DOE OSTI2025

Diffusion and Deformation Mechanism Maps in Li Metal from Atomistic Simulations

The rate of Li transport in the Li metal anode is important for the operation of Li metal-solid state batteries. Here, transport rates due to diffusion and creep are predicted in Li using atomistic simulations. First, molecular dynamics is used to estimate the rate of Li diffusion along dislocations and in grain boundary triple junctions. By combining this data with that from a prior study of grain boundary diffusion the dominant mechanisms and rates of self-diffusion in Li polycrystals are predicted as a function of grain size, grain shape, dislocation density, and temperature. Second, the dominant creep mechanisms are predicted and used to estimate critical current densities and void annihilation times. Grain boundary sliding and coble creep are the dominant mechanisms for micron-sized grains. Lastly, a continuum model for interfacial contact loss reveals that high dislocation densities of ∼10 12 /cm 2 enable achieving battery performance targets for Li grain sizes of ∼10 μm.

Batteries↗