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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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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↗
DOE OSTI2022

Grassmannian Diffusion Maps--Based Dimension Reduction and Classification for High-Dimensional Data

This work introduces the Grassmannian diffusion maps (GDMaps), a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. Here, the method is designed for applications, such as image recognition and data-based classification of constrained high-dimensional data where each data point itself is a high-dimensional object (i.e., a large matrix) that can be compactly represented in a lower-dimensional subspace. The GDMaps is composed of two stages. The first is a pointwise linear dimensionality reduction wherein each high-dimensional object is mapped onto the Grassmann manifold representing the low-dimensional subspace on which it resides. The second stage is a multipoint nonlinear kernel-based dimension reduction using diffusion maps to identify the subspace structure of the points on the Grassmann manifold. To this end, an appropriate Grassmannian kernel is used to construct the transition matrix of a random walk on a graph connecting points on the Grassmann manifold. Spectral analysis of the transition matrix yields low-dimensional Grassmannian diffusion coordinates embedding the data into a low-dimensional reproducing kernel Hilbert space. Further, a novel data classification/recognition technique is developed based on the construction of an overcomplete dictionary of reduced dimension whose atoms are given by the Grassmannian diffusion coordinates. Three examples are considered. First, a "toy" example shows that the GDMaps can identify an appropriate parametrization of structured points on the unit sphere. The second example demonstrates the ability of the GDMaps to revealing the intrinsic subspace structure of high-dimensional random field data. In the last ex- ample, a face recognition problem is solved considering face images subject to varying illumination conditions, changes in face expressions, and occurrence of occlusions. The technique presented high recognition rates (i.e., 95% in the best case) using a fraction of the data required by conventional methods.

42 ENGINEERING↗
DOE OSTI2023

Double Diffusion Maps and their Latent Harmonics for scientific computations in latent space

In this work, we introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion Maps on those latent coordinates allows the approximation of the reduced dynamical models. This second round enables mapping the latent space coordinates back to the full ambient space (what is called lifting); it also enables the approximation of full state functions of interest in terms of the reduced coordinates. In our work, we develop and test three different reduced numerical simulation methodologies, either through pre-tabulation in the latent space and integration on the fly or by going back and forth between the ambient space and the latent space. The data-driven latent space simulation results, based on the three different approaches, are validated through (a) the latent space observation of the full simulation through the Nyström Extension formula, or through (b) lifting the reduced trajectory back to the full ambient space, via Latent Harmonics. Latent space modeling often involves additional regularization to favor certain properties of the space over others, and the mapping back to the ambient space is then constructed mostly independently from these properties; here, we use the same data-driven approach to construct the latent space and then map back to the ambient space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Grassmannian diffusion maps based surrogate modeling via geometric harmonics

Abstract A novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics (GH) is developed for predicting the response of complex physical phenomena. The method utilizes GDMaps to obtain a low‐dimensional representation of the underlying behavior of physical/mathematical systems with respect to uncertain input parameters. Using this representation, GH, an out‐of‐sample extension technique, is employed to create a global map from the input parameter space to a Grassmannian diffusion manifold. GH is further employed to locally map points on the diffusion manifold onto the tangent space of a Grassmann manifold. The exponential map is then used to project the points in the tangent space onto the Grassmann manifold, where reconstruction of the full solution is performed. The performance of the proposed surrogate model is verified with three examples. The first problem is a toy example used to illustrate the technique. In the second example, errors associated with the various mappings are assessed by studying response predictions of the electric potential of a dielectric cylinder in a homogeneous electric field. The last example applies the method for uncertainty prediction in the strain field evolution in a model amorphous material using the shear transformation zone theory of plasticity.

42 ENGINEERING↗
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 OSTI2022

Trajectory design via unsupervised probabilistic learning on optimal manifolds

Abstract This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.

42 ENGINEERING↗
DOE OSTI2022

Manifold Learning-Based Polynomial Chaos Expansions for High-Dimensional Surrogate Models

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction technique which allows us to reduce the dimensionality of the data and identify meaningful geometric descriptions in a parsimonious and inexpensive manner. Polynomial chaos expansion is then used to construct a mapping between the stochastic input parameters and the diffusion coordinates of the reduced space. An adaptive clustering technique is proposed to identify an optimal number of clusters of points in the latent space. The similarity of points allows us to construct a number of geometric harmonic emulators which are finally utilized as a set of inexpensive pretrained models to perform an inverse map of realizations of latent features to the ambient space and thus perform accurate out-of-sample predictions. Thus, the proposed method acts as an encoder-decoder system which is able to automatically handle very high-dimensional data while simultaneously operating successfully in the small-data regime. The method is demonstrated on two benchmark problems and on a system of advection-diffusion-reaction equations which model a first-order chemical reaction between two species. In all test cases, the proposed method is able to achieve highly accurate approximations which ultimately lead to the significant acceleration of UQ tasks.

42 ENGINEERING↗
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↗
DOE OSTI2021

Long-term Dynamical Stability in the Outer Solar System. I. The Regular and Chaotic Evolution of the 34 Largest Trans-Neptunian Objects

We carried out an extensive analysis of the stability of the outer solar system, making use of the frequency analysis technique over short-term integrations of nearly 100,000 test particles, as well as a statistical analysis of 200 1 Gyr long numerical simulations, which consider the mutual perturbations of the giant planets and the 34 largest trans-Neptunian objects (we have called all 34 objects “dwarf planets,” DPs, even if probably only the largest of them are true DPs). From the frequency analysis, we produced statistical diffusion maps for a wide region of the a–e phase-space plane; we also present the average diffusion time for orbits as a function of perihelion. We later turned our attention to the 34 DPs, making an individualized analysis for each of them and producing a first approximation of their future stability. From the 200 distinct realizations of the orbital evolution of the 34 DPs, we classified the sample into three categories, including 17 stable, 11 unstable, and 6 resonant objects; we also found that, statistically, two objects from the sample will leave the trans-Neptunian region within the next gigayear, most likely being ejected from the solar system, but with a nonnegligible probability of going inside the orbit of Neptune, either to collide with a giant planet or even falling to the inner solar system, where our simulations are no longer able to resolve their continuous evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
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.↗