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NASA NTRS1983

Computation of Jupiter interior models from gravitational inversion theory

Spacecraft measurements of Jupiter have provided the mass, standard pressure level radius, rotation law, internal mass distribution multipole moments, and internal composition and temperature distribution constraints, for the present implementation of a method for deriving planetary interior models that exactly satisfy a set of N gravitational constraints by means of appropriate iteration. The models are not forced to fit the more indirectly derived constraints, which are instead used as conistency checks. In the case of an He mass fraction in the envelope Y of 0.2, the inferred pressure at a mass density of about 0.2 g/cu cm is about a factor of 2 higher than would be indicated by experimental H compression data in the relevant pressure range of 100,000 to one million bar. The inferred pressure distribution is in better agreement with the shock data for a nominal Y value of 0.3 + or - 0.05.

Hubbard, W. B.↗
DOE OSTI2022

Bayesian operator inference for data-driven reduced-order modeling

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2019

Full Inversion of Solar Relativistic Electron Events Measured by the Helios Spacecraft

The Parker Solar Probe and the incoming Solar Orbiter mission will provide measurements of solar energetic particle (SEP) events at close heliocentric distances from the Sun. Up to present, the largest data set of SEP events in the inner heliosphere are the observations by the two Helios spacecraft. Aims.We re-visit a sample of 15 solar relativistic electron events measured by the Helios mission with the goal of better characterizing the injection histories of solar energetic particles and their interplanetary transport conditions at heliocentric distances <1AU. Methods. The measurements provided by the E6 instrument on board Helios provide us with the electron directional distributionsin eight di erent sectors that we use to infer the detailed evolution of the electron pitch-angle distributions. The results of a Monte Carlo interplanetary transport model, combined with a full inversion procedure, were used to fit the observed directional intensities in the 300–800 keV nominal energy channel. Unlike previous studies, we have considered both the energy and angular responses of the detector. This method allowed us to infer the electron release time profile at the source and determine the electron interplanetary transport conditions. Results. We discuss the duration of the release time profiles and the values of the radial mean free path, and compare them with thevalues reported previously in the literature using earlier approaches. Five of the events show short injection histories (<30 min) at the Sun and ten events show long-lasting (>30 min) injections. The values of mean free path range from 0.02AU to 0.27AU.Conclusions. The inferred injection histories match with the radio and soft X-ray emissions found in literature.We find no dependence of the radial mean free path on the radial distance. In addition, we find no apparent relation between the strength of interplanetary scattering and the size of the solar particle release.

Pacheco, D.↗
DOE OSTI2022

Making Invisible Visible: Data-Driven Seismic Inversion With Spatio-Temporally Constrained Data Augmentation

Deep learning and data-driven approaches have shown great potential in scientific domains. The promise of data-driven techniques relies on the availability of a large volume of high-quality training datasets. Due to the high cost of obtaining data through expensive physical experiments, instruments, and simulations, data augmentation techniques for scientific applications have emerged as a new direction for obtaining scientific data recently. However, existing data augmentation techniques originating from computer vision yield physically unacceptable data samples that are not helpful for the domain problems that we are interested in. In this article, we develop new data augmentation techniques based on convolutional neural networks. Specifically, our generative models leverage different physics knowledge (such as governing equations, observable perception, and physics phenomena) to improve the quality of the synthetic data. To validate the effectiveness of our data augmentation techniques, we apply them to solve a subsurface seismic full-waveform inversion using simulated CO 2 leakage data. Our interest is to invert for subsurface velocity models associated with very small CO 2 leakage. We validate the performance of our methods using comprehensive numerical tests. Here via comparison and analysis, we show that data-driven seismic imaging can be significantly enhanced by using our data augmentation techniques. Particularly, the imaging quality has been improved by 15% in test scenarios of general-sized leakage and 17% in small-sized leakage when using an augmented training set obtained with our techniques.

58 GEOSCIENCES↗
DOE OSTI2025

Quantification of regional net CO 2 flux errors in the Orbiting Carbon Observatory-2 (OCO-2) v10 model intercomparison project (MIP) ensemble using airborne measurements

Inverse model intercomparison projects (MIPs) provide a chance to assess the uncertainties in inversion estimates arising from various sources. However, accurately quantifying ensemble CO 2 flux errors remains challenging and often relies on the ensemble spread. This study proposes a method for quantifying the errors in regional net surface–atmosphere CO 2 flux estimates from models taken from the Orbiting Carbon Observatory-2 (OCO-2) v10 MIP by using independent airborne CO 2 measurements for the period 2015–2017. We first calculate the root mean square error (RMSE) between the ensemble mean of posterior CO 2 concentrations and airborne observations and then isolate the CO 2 concentration errors caused solely by the ensemble mean of posterior net fluxes by subtracting the observation, representation, and transport errors from seven regions. Our analysis reveals that the flux errors projected onto CO 2 space account for 55 %–85 % of the regional average RMSE over the 3 years, ranging from 0.88 to 1.91 ppm. In five regions, the error estimates based on observations exceed those computed from the ensemble spread of posterior fluxes by a factor of 1.33–1.93, implying an underestimation of the actual flux errors, while their magnitudes are comparable in two regions. The adjoint sensitivity analysis identifies that the underestimation of flux errors is prominent where the magnitudes of fossil fuel emissions exceed those of terrestrial-biosphere fluxes by a factor of 3–31 over the 3 years. This suggests the presence of systematic biases in the inversion estimates associated with errors in the prescribed fossil fuel emissions common to all models. Our study emphasizes the value of airborne measurements for quantifying regional errors in ensemble net CO 2 flux estimates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Multi-fidelity Bayesian neural networks: Algorithms and applications

Here we propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs). These multi-fidelity BNNs consist of three neural networks: The first is a fully connected neural network, which is trained following the maximum a posteriori probability (MAP) method to fit the low-fidelity data; the second is a Bayesian neural network employed to capture the cross-correlation with uncertainty quantification between the low- and high-fidelity data; and the last one is the physics-informed neural network, which encodes the physical laws described by PDEs. For the training of the last two neural networks, we first employ the mean-field variational inference (VI) to maximize the evidence lower bound (ELBO) to obtain informative prior distributions for the hyperparameters in the BNNs, and subsequently we use the Hamiltonian Monte Carlo (HMC) method to estimate accurately the posterior distributions for the corresponding hyperparameters. We demonstrate the accuracy of the present method using synthetic data as well as real measurements. Specifically, we first approximate a one- and four-dimensional function, and then infer the reaction rates in one- and two-dimensional diffusion-reaction systems. Moreover, we infer the sea surface temperature (SST) in the Massachusetts and Cape Cod Bays using satellite images and in-situ measurements. Taken together, our results demonstrate that the present method can capture both linear and nonlinear correlation between the low- and high-fidelity data adaptively, identify unknown parameters in PDEs, and quantify uncertainties in predictions, given a few scattered noisy high-fidelity data. Finally, we demonstrate that we can effectively and efficiently reduce the uncertainties and hence enhance the prediction accuracy with an active learning approach, using as examples a specific one-dimensional function approximation and an inverse PDE problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Composite Bond Line Measurements Based on A Bayesian Analysis of Flash Thermography Data

For bonded composite materials, an accurate characterization of the adhesive bond line is needed to predict failure modes and fracture toughness. In this paper, bond line thickness was estimated from data obtained using through transmission flash thermography. The forward model that predicts back surface temperature is based on a three layer heat diffusion equation with varying diffusivity and flux boundary conditions. The corresponding inverse problem of estimating bond line thickness from measurement data was solved using a Bayesian approach that assumed Gaussian priors for the bond line thickness and thermal diffusivity of the adherends. Finally, the outputs of the thermography based method were compared to measurements that were collected using a micrometer and ultrasound testing.

Flash thermography↗
DOE OSTI2026

Inverse problem in the large momentum effective theory framework

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of 𝑥 where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of 𝜆 = 𝑧⁢𝑃 𝑧 ∼ 5–15, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a “direct” computation of the 𝑥-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the 𝑥-dependence.

Dutrieux, Hervé [Aix-Marseille Université, Marseil↗
DOE OSTI2021

Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Lyα forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of data from SDSS, SDSS-II, BOSS, and eBOSS, offer independent measurements of baryon acoustic oscillation (BAO) measurements of angular-diameter distances and Hubble distances relative to the sound horizon, r d , from eight different samples and six measurements of the growth rate parameter, fσ 8 , from redshift-space distortions (RSD). This composite sample is the most constraining of its kind and allows us to perform a comprehensive assessment of the cosmological model after two decades of dedicated spectroscopic observation. We show that the BAO data alone are able to rule out dark-energy-free models at more than eight standard deviations in an extension to the flat, ΛCDM model that allows for curvature. When combined with Planck Cosmic Microwave Background (CMB) measurements of temperature and polarization, under the same model, the BAO data provide nearly an order of magnitude improvement on curvature constraints relative to primary CMB constraints alone. Independent of distance measurements, the SDSS RSD data complement weak lensing measurements from the Dark Energy Survey (DES) in demonstrating a preference for a flat ΛCDM cosmological model when combined with Planck measurements. The combined BAO and RSD measurements indicate σ 8 =0.85±0.03, implying a growth rate that is consistent with predictions from Planck temperature and polarization data and with General Relativity. When combining the results of SDSS BAO and RSD, Planck, Pantheon Type Ia supernovae (SNe Ia), and DES weak lensing and clustering measurements, all multiple-parameter extensions remain consistent with a ΛCDM model. Regardless of cosmological model, the precision on each of the three parameters, Ω Λ , H 0 , and σ 8 , remains at roughly 1%, showing changes of less than 0.6% in the central values between models. In a model that allows for free curvature and a time-evolving equation of state for dark energy, the combined samples produce a constraint Ω K =-0.0022±0.0022. The dark energy constraints lead to w 0 =-0.909±0.081 and w a =$-0.49_{-0.30}^{+0.35}$, corresponding to an equation of state of w p =-1.018±0.032 at a pivot redshift z p =0.29 and a Dark Energy Task Force Figure of Merit of 94. The inverse distance ladder measurement under this model yields H 0 =68.18±0.79 km s -1 Mpc -1 , remaining in tension with several direct determination methods; the BAO data allow Hubble constant estimates that are robust against the assumption of the cosmological model. In addition, the BAO data allow estimates of H 0 that are independent of the CMB data, with similar central values and precision under a ΛCDM model. Our most constraining combination of data gives the upper limit on the sum of neutrino masses at Σm ν <0.115 eV (95% confidence). Finally, we consider the improvements in cosmology constraints over the last decade by comparing our results to a sample representative of the period 2000-2010. We compute the relative gain across the five dimensions spanned by w, Ω k , Σm ν , H 0 , and σ 8 and find that the SDSS BAO and RSD data reduce the total posterior volume by a factor of 40 relative to the previous generation. Finally, adding again the Planck, DES, and Pantheon SN Ia samples leads to an overall contraction in the five-dimensional posterior volume of 3 orders of magnitude.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

A study of two-pion scattering for the isospin channels, 𝐼 = 0 and 𝐼 = 2, using lattice QCD is presented. Möbius domain-wall fermions, on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions, are used for the lattice computations, which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD Collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of 𝐿 = 4.63 and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states—two pions with a nonzero relative momentum, as well as two pions at rest. Our results for phase shifts for both the 𝐼 = 0 and 𝐼 = 2 channels are consistent with the Roy equation and chiral perturbation theory, though at this preliminary stage our errors for 𝐼 = 0 are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying 𝐾 → 𝜋⁢𝜋 decay, on physical-mass ensembles using the GEVP.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Sparse measurement medical CT reconstruction using multi-fused block matching denoising priors

A major challenge for medical X-ray CT imaging is reducing the number of X-ray projections to lower radiation dosage and reduce scan times without compromising image quality. However these under-determined inverse imaging problems rely on the formulation of an expressive prior model to constrain the solution space while remaining computationally tractable. Traditional analytical reconstruction methods like Filtered Back Projection (FBP) often fail with sparse measurements, producing artifacts due to their reliance on the Shannon-Nyquist Sampling Theorem. Consensus Equilibrium, which is a generalization of Plug and Play, is a recent advancement in Model-Based Iterative Reconstruction (MBIR), has facilitated the use of multiple denoisers are prior models in an optimization free framework to capture complex, non-linear prior information. However, 3D prior modelling in a Plug and Play approach for volumetric image reconstruction requires long processing time due to high computing requirement. Instead of directly using a 3D prior, this work proposes a BM3D Multi Slice Fusion (BM3D-MSF) prior that uses multiple 2D image denoisers fused to act as a fully 3D prior model in Plug and Play reconstruction approach. Our approach does not require training and are thus able to circumvent ethical issues related with patient training data and are readily deployable in varying noise and measurement sparsity levels. In addition, reconstruction with the BM3D-MSF prior achieves similar reconstruction image quality as fully 3D image priors, but with significantly reduced computational complexity. We test our method on clinical CT data and demonstrate that our approach improves reconstructed image quality.

Hossain, Maliha [ORNL]↗
DOE OSTI2024

Prime VI

SAND2025-03757O Prime VI is a distribution-of-disease outbreak model calibration code based on variational inference. It accompanies a publication for submission to Statistics in Medicine journal, and the code will be maintained for open-source use on Sandia's GitLab. The software provides methods for calibrating an epidemiological model to measured case-count data for a multitude of correlated spatial regions. The code solves a Bayesian inverse problem for model calibration where the posterior over-model parameters are approximated through a custom implementation of variational inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Safta, Cosmin↗
DOE OSTI2023

Development of a molecularly informed biogeochemical framework for reactive transport modeling of subsurface carbon inventories, transformations and fluxes (Final Report)

The overall objective of the project was to combine new molecular-level characterization strategies with soil carbon flux measurements to develop and evaluate model representations of subsurface carbon cycling. We expanded on existing studies in the East River watershed, Colorado, in collaboration with the Berkeley Lab Watershed Function Scientific Focus Area (SFA), SLAC Groundwater Quality SFA, and Rocky Mountain Biological Laboratory (RMBL) to develop an elevation and vegetation gradient that is now the subject of long-term monitoring by the USGS. To achieve the overall objective, we combined field studies of soil respiration with laboratory analyses, ranging from spectroscopy to incubation studies. This combination of techniques enabled us to develop a new understanding of the drivers of high-elevation soil respiration. In the process, we developed three new modeling approaches that improve our ability to conceptualize and ultimately to represent soil respiration in numerical models. The first approach is a plot-scale transient inverse model that can be used to determine in situ CO 2 production rates from measured concentration profiles and surface fluxes. Application of this method revealed the importance of plant phenology and deep CO 2 production in moderating CO 2 fluxes to the atmosphere. The second modeling approach is a molecular-scale tool that enables spectroscopic and elemental data for carbon speciation to be transformed into functional group abundances, or the ‘SOC-fga model’. This method uniquely enables carbon speciation to be tracked within a reactive transport framework to partition carbon among different pathways and storage zones within the soil. The third modeling tool builds strongly on the previous approaches and captures the microbial processes driving heterotrophic respiration. This ‘dormancy model’ allows the native soil microbial population to respond transiently to the presence or absence of water in order to catalyze carbon respiration. This approach was also compared to the simpler and more widely used first-order model using two experimental datasets with different temporal and spatial resolutions. Our results illustrate that the simpler first order model provides a robust and efficient representation of deep (>1 meter) soil respiration, but that shallow soils, where most respiration occurs, require explicit representation of moisture-dependent activation and dormancy rates. By assessing soil organic carbon turnover at multiple scales, we see a complex array of controls emerge. Atte scale of a hillslope, spatial heterogeneity in soil respiration rates dominates and is uncorrelated with instantaneous soil moisture and plant community. At the profile scale, the balance between plant inputs and water availability is the dominant control. At the microbial to molecular scale, physiological processes associated with carbon use and carbon speciation are important controls. These scale-dependent controls emphasize the need for new modeling approaches that examine their interactions and hierarchies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

2D Seismic Surveys as an Alternative for CO 2 Monitoring in the North Dakota CarbonSAFE Project

Conference presentation for International Meeting for Applied Geoscience & Energy (IMAGE), Houston, TX, August 28 – September 1, 2023. As part of the North Dakota CarbonSAFE project, seismic, controlled-source electromagnetic, and microgravity baseline monitoring surveys were collected to assess the safe, permanent, commercial-scale geologic storage of CO 2 generated by the Milton R. Young coal-fired power plant. Data from five 2D seismic lines were assessed as an alternative to 3D seismic for CO 2 monitoring. 2D and 3D surveys were compared using wave equation-based (WEB)-AVO inversion. The encouraging WEB-AVO results demonstrated that 2D surveys could be included in CO 2 monitoring programs as a cost-effective method.

20 FOSSIL-FUELED POWER PLANTS↗
NASA NTRS1975

A semiempirical model for atmospheric gamma rays from 0.3 to 10 MeV at a geomagnetic latitude of 40 deg

A model of atmospheric gamma rays based on the concept of source function is proposed for atmospheric depths from 0 to 500 g per sq cm and for an energy range of 0.3-10 MeV at a geomagnetic latitude of 40 deg. Since the source function is derived from measured fluxes, the proposed method is referred to as a semiempirical model. This model derives a source strength directly from measurements with an omnidirectional counter, thereby being an inverse of previous approaches. Source strengths are determined for 38 predicted atmospheric gamma ray lines and for 10 different energies in the continuum. Total and directional fluxes are calculated at two different atmospheric depths. The results are found to be consistent with other measurements and theoretical calculations.

Ling, J. C.↗
NASA NTRS1982

Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

Hamrock, B. J.↗
NASA NTRS1984

Continental and oceanic crustal magnetization modelling

Inversion of magnetic data from the MAGSAT satellite, to arrive at intensities of magnetization of the Earth's crust, was performed by two different methods. The first method uses a spherical harmonic model of the magnetic field. The coefficients believed to represent sources in the Earth's crust can then be inverted to arrive at vertical dipole moments per unit area at the Earth's surface. The spherical harmonic models contain coefficients of degrees of harmonics up to 23. The dipole moment per unit area for a surface element can then be determined by summing the contribution for each individual degree of harmonic. The magnetic moments were calculated for continental and oceanic areas separately as well as over certain latitudinal segments. Of primary concern was to determine whether there are any differences between continental and oceanic areas. The second analysis with magnetization intensities was made using narrower ranges of degrees of harmonics, assuming that higher degrees are present in the core field signal.

Harrison, C. G. A.↗