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440 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Role of the likelihood for elastic scattering uncertainty quantification

In the last decade, uncertainty quantification (UQ) for optical model potentials (OMPs) has become a focal point for nuclear reaction theory, and several competing approaches for OMP UQ have recently been developed. Here, we clarify recent efforts to compare frequentist and Bayesian approaches in the context of OMP UQ [G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019)]. We replicate a portion of that OMP UQ study but use independent statistical tools. Specifically, we compare two methods for OMP parameter inference from elastic scattering data: the Levenberg-Marquardt algorithm for χ 2 minimization on one hand and Markov chain Monte Carlo (MCMC) sampling on the other. Separately, we assess the common practice of using a renormalized likelihood (χ 2 /N), N being the number of data points, instead of the canonical weighted-least-squares likelihood (χ 2 ), as a way of accounting for unknown data correlations. Here, we show that for a generic linear model and for a five-parameter OMP analysis, frequentist and uniform-prior Bayesian approaches recover the same optimum and uncertainty estimates—not systematically larger uncertainties for the Bayesian approach, as was concluded in G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019). Further, we show that if an additional, near-degenerate parameter is introduced into the same OMP analysis such that the parameter posterior becomes non-Gaussian, then covariance-based estimates of uncertainty become unreliable. Finally, we show that regardless of optimization approach, if χ 2 /N is used for the likelihood, the resulting parametric uncertainties increase by $\sqrt{N}$, and that this is responsible for the conclusions drawn in the revisited study. Based on our replication results, we find that a fortuitous cancellation of unreported errors and the renormalization factor can lead to improvement in empirical coverages, as was the case in the original comparative study. We emphasize that developing and applying a realistic likelihood function is an essential task in a UQ analysis, and that several recent UQ studies that employed a renormalized likelihood (i.e., including a 1/N factor) may have yielded unrealistically large uncertainties for elastic-scattering observables. If the parameter posterior deviates from multivariate-normal, a sampling-based approach like MCMC has a clear advantage over methods that assume the Laplace approximation holds. We note that empirical coverage can serve as an important internal check for the analyst whose model or data may have additional, unaccounted-for uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗
DOE OSTI2022

Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk

We present a surrogate modeling framework for conservatively estimating measures of risk from limited realizations of an expensive physical experiment or computational simulation. Risk measures combine objective probabilities with the subjective values of a decision maker to quantify anticipated outcomes. Given a set of samples, we construct a surrogate model that produces estimates of risk measures that are always greater than their empirical approximations obtained from the training data. These surrogate models limit over-confidence in reliability and safety assessments and produce estimates of risk measures that converge much faster to the true value than purely sample-based estimates. We first detail the construction of conservative surrogate models that can be tailored to a stakeholder’s risk preferences and then present an approach, based on stochastic orders, for constructing surrogate models that are conservative with respect to families of risk measures. Our surrogate models include biases that permit them to conservatively estimate the target risk measures. We provide theoretical results that show that these biases decay at the same rate as the L 2 error in the surrogate model. Numerical demonstrations confirm that risk-adapted surrogate models do indeed overestimate the target risk measures while converging at the expected rate.

42 ENGINEERING↗
NASA NTRS2020

Calibrating a 3-Axis Accelerometer Instrument with a Less Accurate Calibration Device Part 1: Mathematical Methodology

A three-axis accelerometer instrument (3xAI) can provide the angular attitude of a 3D object using the gravity vector (g) as the sole reference. Calibrating such an instrument requires placing it at known (to some accuracy plus uncertainty) angular articulations with respect to g. This paper will show a potential process for calibrating a 3xAI by using a 2-axis rotary system (calibration device) to provide these articulations. Any calibration device (CD) with such capacity will contain internal misalignments. These misalignments, even if made relatively small or approximated to zero in the kinematics model (KM), can be detrimental to the calibration of the instrument when high measurement accuracy is required. This is especially true if the selected set of articulations chosen for calibration do not include their symmetrical counterpoints (a point where the misalignment has equal magnitude but is opposite in direction to a point chosen). The consequence of not including the combination, point and counterpoint, for any misalignment involved in the calibration, results in a biased instrument. This paper will demonstrate a calibration of the instrument using symbolic math resulting in a closed-form solution of the instrument coefficients. The main objective is to show the impact of all the CD misalignments to the instrument coefficients. This process is the basis for a more sophisticated method (shown in a future paper) for obtaining the instrument coefficients while simultaneously obtaining an estimate of the calibration device internal misalignments.

Angle↗
NASA NTRS2014

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co-located at one corner. Due to this limited geographical extent, near-surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine- or Lunar Prospector-derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explored the density/velocity relationship. These efforts typically searched for the best fitting thermodynamically calculated velocity/density model, and allowed variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles derived from the Apollo seismic data through travel time inversion vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocity and density as a function of latitude, longitude, and depth within the Moon. We relate density (p) to seismic velocity (v) using a depth-dependent linear relationship. The corresponding coefficient (B) can reflect a variety of material properties, including temperature and composition. The inversion seeks to recover the set of p, v, and B perturbations that minimize (in a least-squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS2013

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps to reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly co‐located at one corner. Due to this limited geographical extent, near‐surface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine‐ or Lunar Prospector‐derived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explore the density/velocity relationship. These efforts typically search for the best fitting thermodynamically calculated velocity/density model, allowing variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles previously derived from the Apollo seismic data through inversion of travel times vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocities and density as a function of latitude, longitude, and depth within the Moon. We will relate density to seismic velocity using a linear relationship that is allowed to be depth‐dependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of density, velocity, and B‐coefficient perturbations that minimize (in a least‐squares sense) the difference between the observed and calculated data.

Weber, Renee C.↗
NASA NTRS2001

Monte Carlo predictions of DNA fragment-size distributions for large sizes after HZE particle irradiation

DSBs (double-strand breaks) produced by densely ionizing space radiation are not located randomly in the genome: recent data indicate DSB clustering along chromosomes. DSB clustering at large scales, from >100 Mbp down to approximately 2 kbp, is modeled using a Monte-Carlo algorithm. A random-walk model of chromatin is combined with a track model, that predicts the radial distribution of energy from an ion, and the RLC (randomly-located-clusters) formalism, in software called DNAbreak. This model generalizes the random-breakage model, whose broken-stick fragment-size distribution is applicable to low-LET radiation. DSB induction due to track interaction with the DNA volume depends on the radiation quality parameter Q. This dose-independent parameter depends only weakly on LET. Multi-track, high-dose effects depend on the cluster intensity parameter lambda, proportional to fluence as defined by the RLC formalism. After lambda is determined by a numerical experiment, the model reduces to one adjustable parameter Q. The best numerical fits to the experimental data, determining Q, are obtained. The knowledge of lambda and Q allows us to give biophysically based extrapolations of high-dose DNA fragment-size data to low doses or to high LETs.

NASA Center JSC↗
DOE OSTI2024

A fast and accurate domain decomposition nonlinear manifold reduced order model

Here, this paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each sub domain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

97 MATHEMATICS AND COMPUTING↗