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DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗

DOE OSTI2025

Optimization of Total Variation-Regularized Problems using Inexact Proximal Solves

Inexact proximal framework for total-variation minimization.

Kouri, Drew Philip [Sandia National Laboratories (↗

NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗

DOE OSTI2025

Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

Source functions are obtained from p – p and d – α correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the p – p and d – α correlation functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRSDate not supplied

Total Variation Majorization Minimization (TV-MM) Approach to Radiometer Brightness Temperature Gridding and Reconstruction

This paper presents the implementation of an algorithm to enhance the image resolution of the Earth's surface brightness temperature (T B ) data measured by radiometers such as the one onboard of the Soil Moisture Active Passive (SMAP) mission. A key step in radiometer T B processing is the conversion of the swath-based calibrated antenna temperature (T A ) measurements to the Level 3 Earth-centered grid. The simplest algorithm to transform this data from swath to gridded format is called drop-in-the-bucket which simply averages surrounding noisy T A samples to form a T B value at the gridded location. This method reduces noise, however produces low resolution products. To obtain a higher resolution product, SMAP uses other techniques such the Backus-Gilbert (BG) algorithm, which is the conventional method used in microwave radiometry. Although this method performs the required interpolation, it is not effective in denoising and removing blurring effects due to antenna filtering of the radiometer image data. Our motivation for this development is to further improve the resolution through post-processing of the radiometer T B image, a highly cost-effective method of image enhancement. The approach adapted in this work is based on the minimization of the Total Variation (TV) regularized objective function that is used extensively in solving general ill-posed linear inverse problems in image processing. Since the TV-based objective function is convex but not everywhere differentiable, there exists many numerical algorithms that can estimate the solution and the one selected for this work is called Majorization- Minimization (MM). By applying this algorithm, simulation experiments were performed based on synthetic data from the Geophysical model as well as real SMAP data to demonstrate the effectiveness of the technique. Results were then compared against the BG method.

Wing Lee↗

DOE OSTI2025

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full-Waveform Inversion

Concrete is a vital material in construction—especially in the nuclear industry, where it is used in critical structures such as containment vessels. Over time, concrete can degrade due to harsh operational and environmental conditions, necessitating that its elastic properties be accurately evaluated to ensure structural integrity and safety. Traditional nondestructive evaluation methods such as ultrasound-based techniques often rely on simplifying assumptions that may not hold true for concrete. This paper presents an advanced ultrasound-based method that uses elastic full-waveform inversion (EFWI) to create detailed images of concrete’s mechanical properties. By accurately modeling wave behaviors such as scattering and reflection, we aim to overcome the limitations of conventional ultrasonic-based methods. In this work, the imaging problem involved reconstructing the various elastic properties of a heterogenous concrete block with three steel rebars embedded in it. The ultrasonic measurements were synthetically generated from multiple sources and receivers, and the reconstruction process was performed using a gradient-based optimization algorithm. Our approach leveraged EFWI to reconstruct high-resolution images of the pressure wave speed, shear wave speed, and density. Multiple misfit functions—including L2-norm, cross-correlation (CC), and L1-norm—combined with total variation (TV) regularization and parameter constraints using a Sigmoid function—were explored for the reconstruction. The results demonstrated that using the L1-norm misfit function in conjunction with TV regularization and Sigmoid constraints significantly improved the reconstruction quality in comparison to traditional methods. This approach provided clearer images with fewer artifacts and better captured background heterogeneity. Our findings highlight that, when properly designed, EFWI carries great potential for providing comprehensive, more accurate, and more reliable assessments of concrete conditions, as is crucial for the maintenance and safety of nuclear power plant structures.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

LATTE: open-source, high-performance traveltime computation, tomography and source location in acoustic and elastic media

Traveltime-based tomography and source location are fundamental approaches for imaging subsurface structures and understanding the spatiotemporal distribution of seismicity from local to global scales. We present an open-source, high-performance framework integrating eikonal equation solvers and adjoint-state theory for traveltime computation, velocity tomography, source location and joint tomography-location in 2-D/3-D acoustic and elastic media. We introduce novel regularization schemes based on total generalized p-variation, structural similarity and multitask machine learning to enhance the fidelity and interpretability of inverted models and source locations. Key features of our implementation also include the ability to leverage both absolute-difference and double-difference traveltime misfits for high-fidelity velocity tomography and source parameter estimation; support for traveltime computation and inversion in diverse 2-D/3-D scenarios with arbitrary source and receiver distributions; and a perturbation-based optimal step-size estimation method to reduce computational costs. In addition, our implementation employs shared-memory and distributed-memory parallelization to provide an efficient solution for traveltime computation, tomography, and source location. In conclusion, we validate the efficacy and accuracy of our approach through multiple synthetic data examples.

58 GEOSCIENCES↗

NASA NTRS1993

A long-term study of H(alpha) line variations in FK Comae Berenices

We present observations of H(alpha) V/R ratio variations in FK Comae Berencies obtained during several observing seasons from 1981 to 1992. The raw H(alpha) emission profile is always observed to be double peaked due to the stellar-absorption component. During the most years the V/R ratio varies regularly with the period of the photometric light curve. The V/R periodicity is most obvious when time spans no longer than several stellar rotations are considered. We propose that the bulk of the emission component of the H(alpha) line arises in corotating circumstellar material that may be similar to that of a quiescent solar prominence. The lifetime of these structures appears to be on the order of weeks. A weak contribution from a circumstellar disk is evident and chromospheric emission may also be present. The appearance or disappearance of circumstellar structures over periods longer than a few weeks, or the total absence of such structures, blurs the more regular variations in H(alpha) seen over short time scales. Other more stochastic activity, such as flares, also clearly occurs. Phase shifts of the V/R ratio from year to year rule out the hypothesis that mass tranfer in a close binary system is responsible for the V/R variations.

Welty, Alan D.↗

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↗

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)↗

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.↗