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DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A Variational Autoencoder Model Toward Molecular Structure Representation Learning of Fuels

Here, in this work, a Variational Autoencoder (VAE)-based data-driven modeling framework is developed with the overarching goal of enabling fuel design. The VAE model is trained on a large dataset with several chemical species to learn a compressed latent space molecular representation. Chemical structure in the form of Simplified Molecular Input Line Entry System (SMILES) string is fed as input, encoded into the VAE latent space, and decoded back to the SMILES string using Long Short-Term Memory (LSTM) networks. Complexities of the VAE training loss function are thoroughly examined by varying the weightage (beta (𝜷) parameter) of the latent space regularization term, thereby assessing the balance between reconstruction accuracy and validity, and focusing on both accurate molecular structure reconstruction and latent space consistency. Two different strategies for 𝜷 variation are evaluated: linear annealing and cyclic annealing. In addition, the impact of total correlation adjustment and hierarchical priors is also studied with regard to the balance between reconstruction fidelity and latent space regularization, and potential issues such as posterior collapse, over-regularization, and poor disentanglement of latent variables. Overall, the best performance of the model is achieved with hierarchical priors and incrementally increasing 𝜷 from 0 to a threshold value of 0.25 over 75 epochs. The generative VAE model can be readily coupled with Quantitative Structure–Property Relationship (QSPR) analysis to develop an integrated end-to-end framework for fuel-property prediction and molecular design of novel promising fuels.

fuel design↗

DOE OSTI2022

Using ultrasonic attenuation in cortical bone to infer distributions on pore size

Here, in this work we infer the underlying distribution on pore radius in human cortical bone samples using ultrasonic attenuation data. We first discuss how to formulate polydisperse attenuation models using a probabilistic approach and the Waterman Truell model for scattering attenuation. We then compare the Independent Scattering Approximation and the higher-order Waterman Truell models’ forward predictions for total attenuation in polydisperse samples. Following this, we formulate an inverse problem under the Prohorov Metric Framework coupled with variational regularization to stabilize this inverse problem. We then use experimental attenuation data taken from human cadaver samples and solve inverse problems resulting in nonparametric estimates of the probability density function on pore radius. We compare these estimates to the “true” microstructure of the bone samples determined via microCT imaging. We find that our methodology allows us to reliably estimate the underlying microstructure of the bone from attenuation data.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Ozone and nitrogen dioxide above the northern Tien Shan

The results of systematic perennial measurements of the total ozone (since 1979) and nitrogen dioxide column (since 1983) in the atmosphere in the European-Asian continent center above the mountainmass of the Tien Shan are given. This region is distinguished by a great number of sunny days during a year. The observation station is at the Northern shore of Issyk Kul Lake (42.56 N 77.04 E 1650 m above the sea level). The measurement results are presented as the monthly averaged atmospheric total ozone and NO2 stratospheric column abundances (morning and evening). The peculiarities of seasonal variations of ozone and nitrogen dioxide atmospheric contents, their regular variances with a quasi-biennial cycles and trends have been noticed. Irregular variances of ozone and nitrogen dioxide atmospheric contents, i.e. their positive and negative anomalies in the monthly averaged contents relative to the perennial averaged monthly means, have been analyzed. The synchronous and opposite in phase anomalies in variations of ozone and nitrogen dioxide atmospheric contents were explained by the transport and zonal circulation in the stratosphere (Kamenogradsky et al., 1990).

Arefev, Vladimir N.↗

DOE OSTI2025

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗

DOE OSTI2024

Rapid Optimization of Total Variation with Applications in Imaging, Additive Manufacturing, and Qualification

Total Variation optimization penalizes the gradient of a control variable or state. While this work focuses on image processing in particular, it has also found applications in inverse problems and topology optimization. In image processing, the goal is to maintain faithfulness to the original image while denoising and/or deblurring. Additionally, bilevel optimization over the spatially varying regularization weights can illuminate interfaces such as damage regions and other anomalies. We will address two fundamental challenges with TV-optimization: (i) the typical slow convergence of existing TV-optimization methods, and (ii) the selection of spatially varying TV parameters to promote interface detection. Additionally, we will apply such techniques to image data collected in additive manufacturing. In said context, stochasticity in build events induces flaws in the manufactured piece, compromising the integrity of said part. There is a critical need for in-situ monitoring to spot anomalies once they form, and in this setting we apply our total variation and hyperparameter solvers. We will develop a customized algorithm based on for extreme-scale TV-optimization that achieves super-linear or quadratic-convergence, a critical property for real-time, image-by-image analysis. A worst-case outcome is a preprocessing step that enhances image quality in-situ, specifically for out-of-focus and noisy images.

36 MATERIALS SCIENCE↗

NASA NTRS1974

Changes in atmospheric composition inferred from ionospheric production rates

Changes in the total electron content of the ionosphere near sunrise are used to determine the integrated production rate in the ionosphere (Q) from 1965 to 1971 at latitudes of 34S, 20N, and 34N. The observed regular semiannual variation in Q through a range of 1:3:1 is interpreted as an increase in the ratio O/N2 (relative densities) near the equinoxes. It follows that there is a worldwide semiannual variation in atmospheric composition, with the above ratio maximum just after the equinoxes. There is a large seasonal variation in the Northern hemisphere with a maximum in mid-summer. This effect is absent in the Southern hemisphere. At all times except solar maximum in the Northern hemisphere there is a global asymmetry. The ratio O/N2 is about three times as large in the Northern hemisphere. The overall mechanism appears to be N2 absorption.

Titheridge, J. E.↗

NASA NTRS1985

Monthly mean distribution of ozone and temperature

Global monthly mean charts for both hemispheres are given for four mid-season months, and for the pressure levels 30, 10, 1, and 0.1 mbar for temperature and 0.4 mbar for ozone. Charts of total ozone are provided separately. This set of charts shows clearly the very close coupling between the temperature and ozone distributions and demonstrates the influence of the large-scale planetary waves which give rise to very large longitudinal variations. The regular and interannual variability of temperature and ozone are discussed.

Labitzke, K.↗

NASA NTRS1992

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

A total variation diminishing (TVD) scheme has been developed and incorporated into an existing time-accurate high-resolution Navier-Stokes code. The accuracy and the robustness of the resulting solution procedure have been assessed by performing many calculations in four different areas: shock tube flows, regular shock reflection, supersonic boundary layer, and shock boundary layer interactions. These numerical results compare well with corresponding exact solutions or experimental data.

Kim, Hyun Dae↗

NASA NTRS1993

A time-accurate high-resolution TVD scheme for solving the Navier-Stokes equations

Kim, Hyun D.↗

NASA NTRS1993

The Galileo solar redshift experiment

From the October 1989 launch to the first December 1990 earth gravity assist, we regularly obtained frequency measurements of the spacecraft clock - an ultrastable crystal oscillator (USO) supplied by Frequency Electronics, Inc. The solar gravitational redshift in frequency was readily detectable, and because of the unique variations in heliocentric distance we could separate the general relativistic effects from the USO's intrinsic frequency variations. We have verified the total frequency shift predicted by general relativity to 0.5 percent accuracy, and the solar gravitational redshift to 1 percent accuracy.

Krisher, Timothy P.↗

NASA NTRS1982

Solar irradiance variations and solar activity

A mean value for the 1 AU total solar irradiance of 1368.2 W/sq m and a downward trend of 0.05% per year were derived from measurements by the Active Cavity Radiometer Irradiance Monitor (ACRIM) experiment on the Solar Maximum Mission during 1980. Distinct temporary solar irradiance decreases associated with solar activity maxima were observed with a series of nine dips from April to October recurring at fairly regular intervals averaging 24 days. The decreases correlate inversely with sunspot area, 2800-MHz flux, and Zurich sunspot number. Dominant periods common to the irradiance and sunspot area power spectra link the irradiance decreases to sunspot flux deficit in solar active regions. Evidence of significant total irradiance modulation by facular flux excess is cited. A persistent radiative cycle of active regions consistent with the ACRIM irradiance results and the morphology of solar active regions was found. The pattern of regularly recurrent active region maxima between April and October suggests an asymmetry in solar activity generation during this period.

Willson, R. C.↗

NASA NTRS2004

Cyclic Oxidation Modeling and Life Prediction

The cyclic oxidation process can be described as an iterative scale growth and spallation sequence by a number of similar models. Model input variable include oxide scale type and growth parameters, spalling geometry, spall constant, and cycle duration. Outputs include net weight change, the amounts of retained and spalled oxide, the total oxygen and metal consumed, and the terminal rates of weight loss and metal consumption. All models and their variations produce a number of similar characteristic features. In general, spalling and material consumption increase to a steady state rate, at which point the retained scale approaches a constant and the rate of weight loss becomes linear. For one model, this regularity was demonstrated as dimensionless, universal expressions, obtained by normalizing the variables by critical performance factors. These insights were enabled through the use of the COSP for Windows cyclic oxidation spalling program.

Smialek, James L.↗

NASA NTRS1999

Postseismic Deformation after the 1964 Great Alaskan Earthquake: Collaborative Research with Goddard Space Flight Center

The purpose of this project was to carry out GPS observations on the Kenai Peninsula, southern Alaska, in order to study the postseismic and contemporary deformation following the 1964 Alaska earthquake. All of the research supported in this grant was carried out in collaboration with Dr. Steven Cohen of Goddard Space Flight Center. The research funding from this grant primarily supported GPS fieldwork, along with the acquisition of computer equipment to allow analysis and modeling of the GPS data. A minor amount of salary support was provided by the PI, but the great majority of the salary support was provided by the Geophysical Institute. After the expiration of this grant, additional funding was obtained from the National Science Foundation to continue the work. This grant supported GPS field campaigns in August 1995, June 1996, May-June and September 1997, and May-June 1998. We initially began the work by surveying leveling benchmarks on the Kenai peninsula that had been surveyed after the 1964 earthquake. Changes in height from the 1964 leveling data to the 1995+ GPS data, corrected for the geoid-ellipsoid separation, give the total elevation change since the earthquake. Beginning in 1995, we also identified or established sites that were suitable for long-term surveying using GPS. In the subsequent annual GPS campaigns, we made regular measurements at these GPS marks, and steadily enhanced our set of points for which cumulative postseismic uplift data were available. From 4 years of Global Positioning System (GPS) measurements, we find significant spatial variations in present-day deformation between the eastern and western Kenai peninsula, Alaska. Sites in the eastern Kenai peninsula and Prince William Sound move to the NNW relative to North America, in the direction of Pacific-North America relative plate motion. Velocities decrease in magnitude from nearly the full plate rate in southern Prince William Sound to about 30 mm/yr at Seward and to about 5 mm/yr near Anchorage. In contrast, sites in the western Kenai peninsula move to the SW, in a nearly trenchward direction, with a velocity of about 20 mm/yr. The data are consistent with the shallow plate interface offshore and beneath the eastern Kenai and Prince William Sound being completely locked or nearly so, with elastic strain accumulation resulting in rapid motion in the direction of relative plate motion of sites in the overriding plate. The velocities of sites in the western Kenai, along strike to the southwest, are opposite in sign with those predicted from elastic strain accumulation. These data are incompatible with a significant locked region in this segment of the plate boundary. Trenchward velocities are found also for some sites in the Anchorage area. We interpret the trenchward velocities as being caused by a continuing postseismic transient from the 1964 great Alaska earthquake.

Freymueller, Jeffrey T.↗

NASA NTRS1989

Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems

Communication requirements of Cholesky factorization of dense and sparse symmetric, positive definite matrices are analyzed. The communication requirement is characterized by the data traffic generated on multiprocessor systems with local and shared memory. Lower bound proofs are given to show that when the load is uniformly distributed the data traffic associated with factoring an n x n dense matrix using n to the alpha power (alpha less than or equal 2) processors is omega(n to the 2 + alpha/2 power). For n x n sparse matrices representing a square root of n x square root of n regular grid graph the data traffic is shown to be omega(n to the 1 + alpha/2 power), alpha less than or equal 1. Partitioning schemes that are variations of block assignment scheme are described and it is shown that the data traffic generated by these schemes are asymptotically optimal. The schemes allow efficient use of up to O(n to the 2nd power) processors in the dense case and up to O(n) processors in the sparse case before the total data traffic reaches the maximum value of O(n to the 3rd power) and O(n to the 3/2 power), respectively. It is shown that the block based partitioning schemes allow a better utilization of the data accessed from shared memory and thus reduce the data traffic than those based on column-wise wrap around assignment schemes.

Naik, Vijay K.↗

NASA NTRS1993

Dwarf novae

Dwarf novae are defined on grounds of their semi-regular brightness variations of some two to five magnitudes on time scales of typically 10 to 100 days. Historically several different classification schemes have been used. Today, dwarf novae are divided into three sub-classes: the U Geminorum stars, the SU Ursae Majoris stars, and the Z Camelopardalis stars. Outbursts of dwarf novae occur at semi-periodic intervals of time, typically every 10 to 100 days; amplitudes range from typically 2 to 5 mag. Within certain limits values are characteristic for each object. Relations between the outburst amplitude, or the total energy released during outburst, and the recurrence time have been found, as well as relations between the orbital period and the outburst decay time, the absolute magnitude during outburst maximum, and the widths of long and short outbursts, respectively. Some dwarf novae are known to have suspended their normal outburst activity altogether for a while. They later resumed it without having undergone any observable changes. The optical colors of dwarf novae all are quite similar during outburst, considerably bluer than during the quiescent state. During the outburst cycle, characteristic loops in the two color diagram are performed. At a time resolution on the order of minutes, strictly periodic photometric changes due to orbital motion become visible in the light curves of dwarf novae. These are characteristic for each system. Remarkably little is known about orbital variations during the course of an outburst. On time-scales of minutes and seconds, further more or less periodic types of variability are seen in dwarf novae. Appreciable flux is emitted by dwarf novae at all wavelengths from the X-rays to the longest IR wavelengths, and in some cases even in the radio. Most dwarf novae exhibit strong emission line spectra in the optical and UV during quiescence, although some have only very weak emissions in the optical and/or weak absorptions at UV wavelengths.

Ladous, Constanze↗

NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗

NASA NTRS1998

Empirical correction for earth sensor horizon radiance variation

A major limitation on the use of infrared horizon sensors for attitude determination is the variability of the height of the infrared Earth horizon. This variation includes a climatological component and a stochastic component of approximately equal importance. The climatological component shows regular variation with season and latitude. Models based on historical measurements have been used to compensate for these systematic changes. The stochastic component is analogous to tropospheric weather. It can cause extreme, localized changes that for a period of days, overwhelm the climatological variation. An algorithm has been developed to compensate partially for the climatological variation of horizon height and at least to mitigate the stochastic variation. This method uses attitude and horizon sensor data from spacecraft to update a horizon height history as a function of latitude. For spacecraft that depend on horizon sensors for their attitudes (such as the Total Ozone Mapping Spectrometer-Earth Probe-TOMS-EP) a batch least squares attitude determination system is used. It is assumed that minimizing the average sensor residual throughout a full orbit of data results in attitudes that are nearly independent of local horizon height variations. The method depends on the additional assumption that the mean horizon height over all latitudes is approximately independent of season. Using these assumptions, the method yields the latitude dependent portion of local horizon height variations. This paper describes the algorithm used to generate an empirical horizon height. Ideally, an international horizon height database could be established that would rapidly merge data from various spacecraft to provide timely corrections that could be used by all.

Hashmall, Joseph A.↗