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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Enabling Hyper-Differential Sensitivity Analysis for Ill-Posed Inverse Problems

Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model that must be estimated. However, high dimensionality of the parameters and computational complexity of the PDE solves make such problems challenging. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to estimate the other parameters. In this article, hyper-differential sensitivity analysis (HDSA) is used to assess the sensitivity of the solution of the PDE-constrained optimization problem to changes in the auxiliary parameters. Foundational assumptions for HDSA require satisfaction of the optimality conditions which are not always practically feasible as a result of ill-posedness in the inverse problem. Here we introduce novel theoretical and computational approaches to justify and enable HDSA for ill-posed inverse problems by projecting the sensitivities on likelihood informed subspaces and defining a posteriori updates. Our proposed framework is demonstrated on a nonlinear multiphysics inverse problem motivated by estimation of spatially heterogeneous material properties in the presence of spatially distributed parametric modeling uncertainties.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗
DOE OSTI2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be ${12.39}_{-0.98}^{+1.30}$ km and ${2.072}_{-0.066}^{+0.067}$ M ⊙ respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is ${\mathrm{log}}_{10}(T\,[{\rm{K}}])={5.99}_{-0.06}^{+0.05}$ for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Furthermore, our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters (within the prior support) and can thus be computed from the posterior samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in Sn 116 , 118 , 120 , 122 , 124 , 130 , 132 , Pb 208 , and Ca 48

The neutron skin thickness Δr np in heavy nuclei has been known as one of the most sensitive terrestrial probes of the nuclear symmetry energy E sym (ρ) around $\frac{2}{3}$ of the saturation density ρ 0 of nuclear matter. Existing neutron skin data mostly from hadronic observables suffer from large uncertainties and their extraction from experiments are often strongly model dependent. While waiting eagerly for the promised model-independent and high-precision neutron skin data for 208 Pb and 48 Ca from the parity-violating electron scattering experiments (PREX-II and CREX at JLab as well as MREX at MESA), within the Bayesian statistical framework using the Skyrme-Hartree-Fock model we infer the posterior probability distribution functions (PDFs) of the slope parameter L of the nuclear symmetry energy at ρ 0 from imagined Δr np ( 208 Pb)=0.15, 0.20, and 0.30 fm with a 1σ error bar of 0.02, 0.04, and 0.06 fm, respectively, as well as Δr np ( 48 Ca)=0.12, 0.15, and 0.25 fm, with different 1σ error bar of 0.01 and 0.02 fm, respectively. The results are compared with the PDFs of L inferred using the same approach from the available Δr np data for 116, 118, 120, 122, 124, 130, 132 Sn from hadronic probes. They are also compared with results from a recent Bayesian analysis of the radius and tidal deformability data of canonical neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes gives L = 45.5 $^{+ 26.5}_{-21.6}$ MeV surrounding its mean value or L = 53 . 4 $^{+ 18.6}_{ -29.5}$ MeV surrounding its maximum a posteriori value, respectively, with the latter smaller than but consistent with the L = 66 $^{+ 12}_{-20}$ MeV from the neutron star data within their 68% confidence intervals. We found that Δr np = 0.17 –0.18 fm in 208 Pb with an error bar of about 0.02 fm leads to a PDF of L compatible with that from analyzing the Sn data. To provide additionally useful information on L extracted from the Δr np of Sn isotopes, the experimental error bar of Δr np in 208 Pb should be at least smaller than 0.06 fm aimed by some current experiments. In addition, the Δr np ( 48 Ca) needs to be larger than 0.15 fm but smaller than 0.25 fm to be compatible with the Sn and/or neutron star results. To further improve our current knowledge about L and distinguish its PDFs in the examples considered, even higher precisions leading to significantly less than ±20 MeV error bars for L at 68% confidence level are necessary.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Evaluating quenching in cosmological simulations of galaxy formation with spectral covariance in the optical window

ABSTRACT Cosmological hydrodynamical simulations provide valuable insights on galaxy evolution when coupled with observational data. Comparisons with real galaxies are typically performed via scaling relations of the observables. Here, we follow an alternative approach based on the spectral covariance in a model-independent way. We build upon previous work by Sharbaf et al. that studied the covariance of high-quality SDSS (Sloan Digital Sky Survey) continuum-subtracted spectra in a relatively narrow range of velocity dispersion ($\sigma \in [100,150]$ km s$^{-1}$). Here, the same analysis is applied to synthetic data from the eagle and IllustrisTNG100 simulations, to assess the ability of these runs to mimic real galaxies. The real and simulated spectra are consistent regarding spectral covariance, although with subtle differences that can inform the implementation of subgrid physics. Spectral fitting done a posteriori on stacks segregated with respect to latent space reveals that the first principal component (PC1) is predominantly influenced by the stellar age distribution, with an underlying age–metallicity degeneracy. Good agreement is found regarding star formation prescriptions but there is disagreement with active galactic nucleus (AGN) feedback, that also affects the subset of quiescent galaxies. We show a substantial difference in the implementation of the AGN subgrid prescriptions, regarding central black hole seeding, that could lead to the mismatch. Differences are manifest between these two simulations in the star formation histories stacked with respect to latent space. We emphasize that this methodology only relies on the spectral covariance to assess whether simulations provide a true representation of galaxy formation.

Sharbaf, Z. (ORCID:0009000450545946)↗
DOE OSTI2022

Characterization and Valuation of the Uncertainty of Calibrated Parameters in Microsimulation Decision Models

We evaluated the implications of different approaches to characterize the uncertainty of calibrated parameters of microsimulation decision models (DMs) and quantified the value of such uncertainty in decision making. We calibrated the natural history model of CRC to simulated epidemiological data with different degrees of uncertainty and obtained the joint posterior distribution of the parameters using a Bayesian approach. We conducted a probabilistic sensitivity analysis (PSA) on all the model parameters with different characterizations of the uncertainty of the calibrated parameters. We estimated the value of uncertainty of the various characterizations with a value of information analysis. We conducted all analyses using high-performance computing resources running the Extreme-scale Model Exploration with Swift (EMEWS) framework. The posterior distribution had a high correlation among some parameters. The parameters of the Weibull hazard function for the age of onset of adenomas had the highest posterior correlation of -0.958. When comparing full posterior distributions and the maximum-a-posteriori estimate of the calibrated parameters, there is little difference in the spread of the distribution of the CEA outcomes with a similar expected value of perfect information (EVPI) of $\$$653 and $\$$685, respectively, at a willingness-to-pay (WTP) threshold of $\$$66,000 per quality-adjusted life year (QALY). Ignoring correlation on the calibrated parameters’ posterior distribution produced the broadest distribution of CEA outcomes and the highest EVPI of $\$$809 at the same WTP threshold. Different characterizations of the uncertainty of calibrated parameters affect the expected value of eliminating parametric uncertainty on the CEA. Ignoring inherent correlation among calibrated parameters on a PSA overestimates the value of uncertainty.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Modeling MTS pyrolysis and SiC deposition kinetics using principal component analysis and neural networks

Accurate chemical kinetics modeling is crucial for improving the efficiency of chemical processing and synthesis of ceramic matrix composites. Detailed kinetic models are computationally expensive due to the large number of transported chemical species, while the simplified physics-based models, such as single-step global mechanisms, are efficient but often overlook key chemical intermediates and pathways. Recent deep learning approaches promise accurate and cost-effective models. Yet, they require additional closures for the transported nonlinear latent variables, complicating integration with existing solvers. In this work, we develop a hybrid linear—nonlinear reduced model for silicon carbide deposition from methyltrichlorosilane precursor by combining principal component analysis (PCA) and autoencoder (AE) neural network (NN) approaches. PCA is used to identify a smaller set of linear transport variables, enabling direct reuse of conventional transport solvers. NNs then reconstruct the full chemical state from these reduced variables. We demonstrate the method on a chemical vapor deposition reactor—comprising a gas-phase pyrolysis plug flow reactor and a heterogeneous surface reactor—over a wide range of temperatures, pressures, and residence times. Our PCA–AE model achieves high accuracy with only five transported scalars, achieving an eightfold cost reduction compared to detailed mechanisms, in both a priori (using data from the test set only) and a posteriori (coupled with a differential equation solver). In conclusion, notable errors arise primarily near training domain boundaries and for long residence times, indicating the need for domain shift indicators and better long-horizon predictions in future reduced chemistry model development.

autoencoder neural networks↗
DOE OSTI2024

Enhancing the Range and Reliability of the Spacer Layer Imaging Method

The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.

EHL film geometry↗
DOE OSTI2020

Provable Convergence of Plug-and-Play Priors With MMSE Denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. Here we address this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Bayesian estimation of cross-section and errors of experiment and calculation for accurate prediction of neutronic characteristics

In some experiments, there might be a correlation of experimental errors such as an error caused by fabrication. The correlation of calculation errors also might exist among analyses of experiments. In the present study, considering these correlations, the cross-section and errors of experiment and calculation are adjusted for the accurate prediction of neutronic characteristics. The adjustment method is derived based on Bayesian theory. The 'a posteriori' distributions of cross-section and errors of experiment and calculation are obtained by the derivation. The case study is performed by using the benchmarks of light-water moderated experiments reported in ICSBEP. The error from fuel rod fabrication and measurement are included in the experiment error, and the error from the simplification of the benchmark model is included in the calculation error. Since these errors have a positive correlation among the benchmarks, the prediction accuracy is expected to be improved by considering these correlations. For the sensitivity analysis of the correlation among benchmarks, the correlation coefficient of experiment error and that of calculation error is assumed from 0.0 to 0.9. The results indicate that the prediction accuracy of the multiplication factor can be improved by increasing the correlation coefficient of experiment error and that of calculation error. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

An approximate inertial manifold (AIM) based closure for turbulent flows

A closure model for turbulent flows is developed based on a dynamical system theory. An appropriately discretized formulation of the governing equations is considered for this process. The key ingredient is an approximation of the system’s attractor, where all the trajectories in phase space are confined. This approximate inertial manifold based approach provides a path to track trajectories of the system in a lower-dimensional subspace. Unlike conventional coarse-graining approaches, the turbulent field is decomposed into resolved and unresolved dynamics using the properties of the governing equations. The novelty of the approach relies on the reconstruction of the unresolved field constrained by the governing equations. A posteriori tests for homogeneous isotropic turbulence and the Kuramoto–Sivashinsky equation show promising results for considerable dimension reduction with strong convergence properties. The proposed model outperforms the dynamic Smagorinsky model, and the computational overhead is competitive with similar approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Autoencoder Neural Network for chemically reacting systems

Incorporating detailed chemical kinetic models is critical for accurate simulations of reacting flows. However, detailed models involve a large number of thermochemical (TC) state variables. Solving the governing equations to evolve these TC variables becomes impractical for real-world applications. In this work, we propose an autoencoder (AE) neural network (NN)-based reduced model to accelerate such simulations. The AE NN is first trained to find a low-dimensional latent representation of the TC states. Then, the evolving state of a chemical system can be tracked by solving the equations of the latent variables instead of the original TC equations. We demonstrate the reduced model in a syngas CO/H 2 combustion system, using training data collected from canonical perfectly stirred reactors (PSRs). It is found that the AE model can reduce the dimension of the combustion system from 12 to 2 while maintaining low reconstruction error and excellent elemental mass conservation for the test dataset. In the a posteriori test, the combustion states obtained from solving the two latent equations are compared to those from solving the 12 equations of the full model. The AE reduced method is found to be able to capture the diverse combustion states on the top two branches of the S-curve well including the extinction turning point, but with higher prediction errors for states near the ignition turning point.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Closures for multicomponent reacting flows based on dispersion analysis

This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and diffusion. Expanding upon analysis originally developed for non-reactive transport in the context of Taylor dispersion of scalars, this work extends the modified gradient diffusion model explicated by Peters [N. Peters, Turbulent Combustion, Cambridge Monographs on Mechanics (Cambridge University Press, Cambridge, 2000)] and based on work by Corrsin [S. Corrsin, The reactant concentration spectrum in turbulent mixing with a first-order reaction, J. Fluid Mech. 11, 407 (1961)] beyond single-component transport phenomena and involving nonlinear reactions. The presented model forms, from this weakly nonlinear extension of the original dispersion theory, lead to an analytic expression for the eddy diffusivity matrix that explicitly captures the influence of the reaction kinetics on the closure operators. Furthermore, we demonstrate that the derived model form directly translates between flow topologies through a priori and a posteriori testing of a binary species system subject to homogeneous isotropic turbulence. Using two- and three-dimensional direct numerical simulations involving laminar and turbulent flows, it is shown that this framework improves prediction of mean quantities compared to previous results. Lastly, the presented model form, collapses to the earlier gradient diffusion and its modified version derived by Corrsin in the limits of nonreactive species and linear reactions, respectively.

42 ENGINEERING↗
DOE OSTI2023

Application of Principal Component Analysis to Electrochemical Reprocessing PM and NMAC

In this report, data from an electrorefiner (ER) for nuclear fuel reprocessing is evaluated for process monitoring (PM) conclusions. This data comes from tests performed at the Idaho National Laboratory in 2022. Multivariate approaches utilizing methods of Principal Component Analysis (PCA) is applied. This is based off established work in process monitoring for fault detection in industrial facilities. This report will discuss the background, methods, and results of the application and some of the conclusions and applications that can be drawn from them. PCA is applied to two different electrorefiner (ER) operations that occurred at Idaho National Laboratory between August and October 2022. The first operation occurred with little incident while the second had several noted faults in the equipment in operational logs. The data from the first run was used to train the data for “normal” operations and applied to both sets of data to determine when operations were in an “off-normal” condition and identify where the fault occurs through PCA. PCA was able to identify off-normal events and identify the cause for off-normal operations. These identified off-normal events matched with the events and their causes in the operational logs. However, small amounts of variance in the data led to false detection of “off-normal” events. Thus, careful selection of training data and a-posteriori conclusions based off operator assessments will both be required for application of PCA to PM applications. This work demonstrated that multivariate approaches and latent variables are applicable to pyroprocessing PM applications and can be further expanded in future work as quality variables such as salt concentration from sensors and sampling become available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Fossil fuel CO 2 emissions over metropolitan areas from space: A multi-model analysis of OCO-2 data over Lahore, Pakistan

Urban areas, where gathering more than 55% of the global population, alone contributed to more than 70% of anthropogenic fossil fuel carbon dioxide (CO 2ff ) emissions. Accurate quantification of CO 2ff emissions from urban areas is of great importance to the formulation of global warming mitigation policies to achieve carbon neutrality by 2050. Satellite-based inversion techniques are unique among “top-down” approaches, potentially allowing us to track CO 2ff emission changes over cities globally. However, its accuracy is still limited by incomplete background information, cloud blockages, aerosol contaminations, and uncertainties in models and emission inventories used as prior. To evaluate the current potential of space-based quantification techniques, we present the first attempt to monitor long-term changes in CO 2ff emissions based on the OCO-2 satellite measurements of column-averaged dry-air mole fractions of CO 2 (X CO2 ) over a fast-growing Asian metropolitan area: Lahore, Pakistan. We first examined the OCO-2 data availability at global scale. About 17% of OCO-2 soundings are marked as high-quality soundings by quality flags over the global 70 most populated cities over the period 2014-2019. Cloud blockage and aerosol contamination are the two main causes of data loss. As an attempt to recover additional soundings, we evaluated the effectiveness of OCO-2 quality flags at the city level by comparing three flux quantification methods (WRF-Chem, X-STILT, and flux cross-sectional integration method), all based on the Open-Data Inventory for Anthropogenic Carbon dioxide (ODIAC) product. The satellite/bottom-up emissions (OCO-2/ODIAC) ratios of the high-quality tracks better converged across the three methods compared to the all-data tracks with reduced uncertainties in emissions. Thus, OCO-2 quality flags are useful filters of low-quality OCO-2 retrievals at local scales, although originally designed for global-scale studies. All three methods consistently suggested that the ratio medians are greater than 1, which implies that the ODIAC slightly underestimated the CO2ff emissions over Lahore. Additionally, our estimation of the a posteriori CO2ff emission trend was about 734 kt C/year (i.e., an annual 6.7% increase). 10,000 Monte Carlo simulations of the Mann-Kendall upward trend test showed that less than 10% prior uncertainty for 8 tracks (or less than 20% prior uncertainty for 25 tracks) is required to achieve a greater-than-50% trend significant possibility at a 95% confidence level. It implies that the trend is driven by the prior and not due to the assimilation of OCO-2 retrievals. The key to improving the role of satellite data in CO 2 emission trend detection lies in collecting more frequent high-quality tracks near metropolitan areas to achieve significant constraints from X CO2 retrievals.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Measuring and simulating ice–ablator mix in inertial confinement fusion

Fuel–ablator mix has been established as a major performance degrading effect in the burning plasma regime of recent inertial confinement fusion (ICF) experiments. As such, the study of fuel–ablator mix with experiments and simulations can provide valuable insight for our understanding of these experiments and establish a path for even higher yields and increased robustness. Here we present a novel high-yield experimental ICF design that is motivated by recent experiments measuring ice–ablator mix with a CH ablator instead of a high-density carbon (HDC) ablator. Here we review these experiments in more detail and describe the modeling assumptions and parameters used to obtain agreement with the data from implosion and burn simulations with mix. Using this mix model calibrated a posteriori to the experimental data, we design an implosion that uses a CH ablator that is predicted to achieve better performance than a recent experiment that achieved net target gain of 1.5 in HDC. Because hydrodynamic instabilities are greatly reduced with this new design, we also expect a high reproducibility at the same implosion adiabat as current record yield experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On unifying randomized methods for inverse problems

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems with Gaussian priors by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a sample average approximation (SAA). More importantly, we are able to prove a single theoretical result that guarantees the asymptotic convergence for a variety of randomized methods. Additionally, viewing randomized methods as an SAA enables us to prove, for the first time, a single non-asymptotic error result that holds for randomized methods under consideration. Another important consequence of our unified framework is that it allows us to discover new randomization methods. Here, we present various numerical results for linear, nonlinear, algebraic, and PDE-constrained inverse problems that verify the theoretical convergence results and provide a discussion on the apparently different convergence rates and the behavior for various randomized methods.

42 ENGINEERING↗