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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 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 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

Novel pore size-controlled, susceptibility matched, 3D-printed MRI phantoms

We report the design concept and fabrication of MRI phantoms, containing blocks of aligned microcapillaires that can be stacked into larger arrays to construct diameter distribution phantoms or fractured, to create a “powder-averaged” emulsion of randomly oriented blocks for vetting or calibrating advanced MRI methods, that is, diffusion tensor imaging, AxCaliber MRI, MAP-MRI, and multiple pulsed field gradient or double diffusion-encoded microstructure imaging methods. The goal was to create a susceptibility-matched microscopically anisotropic but macroscopically isotropic phantom with a ground truth diameter that could be used to vet advanced diffusion methods for diameter determination in fibrous tissues. Two-photon polymerization, a novel three-dimensional printing method is used to fabricate blocks of capillaries. Double diffusion encoding methods were employed and analyzed to estimate the expected MRI diameter. Susceptibility-matched microcapillary blocks or modules that can be assembled into large-scale MRI phantoms have been fabricated and measured using advanced diffusion methods, resulting in microscopic anisotropy and random orientation. This phantom can vet and calibrate various advanced MRI methods and multiple pulsed field gradient or diffusion-encoded microstructure imaging methods. We demonstrated that two double diffusion encoding methods underestimated the ground truth diameter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1995

The double oval UV auroral distribution. 1: Implications for the mapping of auroral arcs

During the later stages of the auroral substorm the luminosity distribution frequently resembles a double oval, one oval lying poleward of the normal or main UV auroral oval. We interpret the double oval morphology as being due to the plasma sheet boundary layer becoming active in the later stages of the substorm process. If the disturbance engulfs the nightside low-latitude boundary layers, then the double oval configuration extends into the dayside ionospheric region. The main UV oval is associated with the inner portion of the central plasma sheet and can rapidly change its auroral character from being diffuse to discrete. This transition is associated with the substorm process and is fundamental to understanding the near-Earth character of substorm onset. On the other hand, the poleward arc system in the nightside ionosphere occurs adjacent to or near the open-closed field line boundary. This system activates at the end of the optical expansion phase and is a part of the recovery phase configuration in substorms where it occurs. These two source regions for nightside discrete auroral arcs are important in resolving the controversy concerning the mapping of arcs to the magnetosphere. The dayside extension of this double oval configuration is also investigated and shows particle signatures which differ considerably from those on the nightside giving clues to the magnetospheric source regions of the aurora in the two local time sectors. Near-Earth substorm onsets are shown to be coupled to processes occurring much further tailward and indicate the importance of understanding the temporal development of features within the double oval. Using 'variance images,' a new technqiue for the investigation of these dynamics is outlined.

Elphinstone, R. D.↗

NASA NTRS1986

Einstein observations of the soft X-ray background close to the Galactic plane

A map of the soft X-ray emission along a Galactic meridian within + or - 3 deg of the Galactic plane is presented. An excess of diffuse M-band emission is found at low latitudes which exhibits a resolved, double-peaked profile that is roughly symmetric about b = 0 deg with a half-width about 1-2 deg. The integrated intensity derived for that band for this component is roughly 3-4 times the dip in intensity expected due to absorption of the extragalactic background in the plane at these energies. Assuming that this excess is characteristic of the whole Galactic plane, model fits are performed so as to derive constraints on the scale height and volume emissivity of the X-ray emitting material. The present results are compared with those inferred from observations of the harder 2-10 keV background.

Kahn, S. M.↗

DOE OSTI2024

Tunable Growth of Layered Double Hydroxide Nanosheets through Hydrothermal Conversion of Atomic Layer Deposition Seed Layers

To enable the design and manufacturing of hierarchical nanomaterial architectures, there is a need for synthesis and processing methods that can enable tunable geometric control at the nanoscale while maintaining conformality on complex 3-D templates. Here, in this study, we explore the programmable control of vertically oriented Zn-Al layered double hydroxide (LDH) nanosheet arrays using atomic layer deposition (ALD) to deposit a seed layer of Al 2 O 3 , which is subsequently consumed and converted into the LDH phase under hydrothermal growth conditions. We demonstrate tunable control over the spacing and length of the nanosheets by varying the thickness of the initial ALD seed layer with subnanometer precision. This can be viewed as a nanoscale titration reaction, where Al acts as the limiting reagent during the hydrothermal synthesis of the nanosheets. Elemental mapping demonstrates the dynamic evolution of the resulting morphology, which is driven by surface diffusion and nucleation processes. The conformal nature of ALD allows for hierarchical growth of nanosheets on the surface of a variety of nonplanar substrate geometries, including microposts, paper fibers, and porous ceramic supports. This illustrates the power of ALD to enable bottom-up growth of 3-D nanoarchitectures with tunable geometries by controlling nucleation and growth in subsequent solution reactions.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Imaging crossing fibers in mouse, pig, monkey, and human brain using small-angle X-ray scattering

Myelinated axons (nerve fibers) efficiently transmit signals throughout the brain via action potentials. Multiple methods that are sensitive to axon orientations, from microscopy to magnetic resonance imaging, aim to reconstruct the brain's structural connectome. As billions of nerve fibers traverse the brain with various possible geometries at each point, resolving fiber crossings is necessary to generate accurate structural connectivity maps. However, doing so with specificity is a challenging task because signals originating from oriented fibers can be influenced by brain (micro)structures unrelated to myelinated axons. X-ray scattering can specifically probe myelinated axons due to the periodicity of the myelin sheath, which yields distinct peaks in the scattering pattern. Here, in this work, we show that small-angle X-ray scattering (SAXS) can be used to detect myelinated, axon-specific fiber crossings. We first demonstrate the capability using strips of human corpus callosum to create artificial double- and triple-crossing fiber geometries, and we then apply the method in mouse, pig, vervet monkey, and human brains. We compare results to polarized light imaging (3D-PLI), tracer experiments, and to outputs from diffusion MRI that sometimes fails to detect crossings. Given its specificity, capability of 3-dimensional sampling and high resolution, SAXS could serve as a ground truth for validating fiber orientations derived using diffusion MRI as well as microscopy-based methods.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1986

Blazars with arcminute-scale radio halos

About 10-arcsec resolution 20-cm wavelength maps are presented for three nearby BL Lac objects: Mkn 180, whose halo has a linear size of 85 kpc, 2155-304, with a halo about 375 kpc across, and 1727 + 502, whose one-sided diffuse emission extends to a distance of about 145 kpc from its radio core. Little evidence is found for strong radio variability in the cores of the three blazars; these and other results obtained are consistent with the assertion that the three objects should be classified as normal low luminosity double radio galaxies with optically dull nuclei, if seen from other directions.

Ulvestad, J. S.↗

NASA NTRS2003

A Self-Contained Mapping Closure Approximation for Scalar Mixing

Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.

He, Guo-Wei↗

NASA NTRS1979

Investigations of coherent anti-Stokes Raman spectroscopy /CARS/ for combustion diagnostics

Investigations of coherent anti-Stokes Raman spectroscopy (CARS) in a variety of flames are presented. Thermometry has received the primary emphasis in these studies, but species spectral and sensitivity studies will also be described. CARS is generated by mixing a 10 pps, frequency-doubled neodymium 'pump' laser with a spectrally broadband, laser-pumped, Stokes-shifted dye laser. This approach obviates the requirement to frequency scan the dye laser and generates the entire CARS spectrum with each pulse permitting, in principle, instantaneous measurements of medium properties. CARS spectra of N2, CO, O2, H2O, CO2 and CH4 in flames will be presented. In general these spectra exhibit very good agreement with computer synthesized spectra and permit measurements of temperature and species concentration. To illustrate the applicability of CARS to practical combustion diagnostics, CARS signatures from N2 have been employed to map the temperature field throughout a small, luminous, highly sooting propane diffusion flame

Eckbreth, A. C.↗

NASA NTRS2005

Lunar and Planetary Science XXXVI, Part 20

The topics include: 1) Virtual Reality Technology as a Tool to Enhance Collaboration Between Space Exploration and Public Outreach: The Case Using the Mars Exploration Rover Images; 2) Atmospheric Electron-induced X-Ray Spectrometer (AEXS) Instrument Development; 3) Impact of Low Thermal Conductivity Layers on the Bulk Conductivity of a Martian Crustal Column; 4) Impacting Classroom Teachers Through Long-Term Professional Development; 5) Oxygen, Ca, and Ti Isotopic Compositions of Hibonite-bearing Inclusions; 6) Phenomenological Excitation Functions of Xe Isotopes with Protons on Nuclei of Cs, La and Ce; 7) Double-Diffusive Convection and Other Modes of Salinity-modulated Heat and Material Transport in Europa s Ocean; 8) Slope Morphologies of the Hellas Mensae Constructs, Eastern Hellas Planitia, Mars; 9) Development of Polygonal Thermal Contraction Patterns in a South Polar Trough, Mars 3 Years of Observations; 10) Martian Relevance of Dehydration and Rehydration in the Mg-Sulfate System; 11) Formation of Martian Volcanic Provinces by Lower Mantle Flushing? 12) Can Glasses Help Us to Unravel the Origin of Barred Olivine Chondrules? 13) Loki Patera: A Magma Sea Story; 14) Compositions of Partly Altered Olivine and Replacement Serpentine in the CM2 Chondrite QUE93005; 15) Model of Light Scattering by Lunar Regolith at Moderate Phase Angles: New Results; 16) Radiation Resistance of a Silicone Polymer Grease Based Regolith Collector for the HERA Near-Earth Asteroid Sample Return Mission; 17) Analysis of the Tectonic Lineaments in the Ganiki Planitia (V14) Quadrangle, Venus; 18) Nanometer-sized Diamonds from AGB Stars; 19) Quantifying Exact Motions Along Lineaments on Europa; 20) Geometry of Thrust Faults Beneath Amenthes Rupes, Mars; 21) Mapping of the Physical Characteristics and Mineral Composition of a Superficial Layer of the Moon or Mars and Ultra-Violet Polarimetry from the Orbital Station; 22) Negative Searches for Evidence of Aqueous Alteration on Asteroid Surfaces; 23) What Processes Have Shaped Basalt Boulders on Earth and Mars? Studies of Feature Persistence Using Facet Mapping and Fractal Analysis; 24) The Popigai Fluidizites: Dense Water Inclusions in Lechatelierite; Evidence for Shock-generated Carbonate and Hydrous Silicate Melts; 25) Missing Xenon Problem and Climate of the Early Earth; and 26) More on Magnetic Spectra from Correlated Crustal Sources on Mars

Source record↗

DOE OSTI2026

Pore-Scale Transport Effects in Electrochemical CO 2 Reduction on Gold via Coupled Microkinetic-Transport Modeling

A pore-resolved modeling framework is developed to quantify how pore-scale transport affects the intrinsic microkinetics of CO 2 -to-CO on Au. A DFT-informed microkinetic model is coupled self-consistently to a Generalized-Modified Poisson–Nernst–Planck (GMPNP) transport description in a single, electrolyte-filled cylindrical pore, allowing local concentrations and potential to feed back into site-specific reaction rates. FIB-SEM is used to determine pore sizes within realistic electrode materials. Across pore diameters, d p = 10–6000 nm, the surface-averaged CO 2 reduction rate is systematically reduced relative to the ideal microkinetic baseline where mass transport is not accounted for; the effectiveness factor 𝜂 𝑠,CO 2 , which quantifies this ratio, decreases rapidly at more negative potentials and is about 1% near −1.0 V vs SHE due to reactant depletion. Spatial maps reveal pore-bulk alkalization that emerges at higher cathodic bias, with a small, near-wall pH dip due to electrostatic repulsion of hydroxide at the cathode interface. For a fixed aspect ratio L p /d p , narrower pores exhibit larger 𝜂 𝑠,CO 2 by shortening diffusion paths, whereas variations in the aspect ratio L p /d p play a secondary role. A dimensionless analysis (surface/bulk Damköhler numbers) delineates operating regimes. In conclusion, this work offers a concept for incorporating microkinetic models into homogenized porous-electrode models through effectiveness factors and pore-size distribution.

Au-catalyst↗