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Results for “Inverse Problems”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Applying a predictive modeling methodology to a radiation transport inverse problem - 25588

In this paper, the predictive modeling of coupled multiphysics systems (PM-CMPS) procedure, developed by Cacuci and embodied in the software package MULTIPRED, has been applied to determine unknown parameters of a radioactive system from its gamma-ray and neutron signature. PM-CMPS has been integrated in two different ways with the inverse transport code INVERSE to determine the parameters. The first uses PM-CMPS in the inverse mode to directly estimate the parameters while the second mode uses a traditional nonlinear optimization routine and has PMCMPS complete a final iteration to estimate the uncertainty in the parameter best estimates. A test problem has been created and used to test both methods for varying numbers and types of responses and parameters. The first method was capable of accurately determining parameters but had a number of drawbacks. The second method functioned well at determining the correct parameter values in cases with limited numbers of parameters. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
NASA NTRS1971

Inversion problem for ion-atom differential elastic scattering.

The paper describes a practical application of Remler's (1971) method by which one constructs a set of phase shifts from high resolution measurements of the differential elastic scattering of protons by rare-gas atoms. These JWKB phase shifts are then formally inverted to determine the corresponding intermolecular potentials. The validity of the method is demonstrated by comparing an intermolecular potential obtained by direct inversion of experimental data with a fairly accurate calculation by Wolniewicz (1965).

Rich, W. G.↗
NASA NTRS1990

Sedimentary Facies Analysis Using AVIRIS Data: A Geophysical Inverse Problem

AVIRIS data can be used to quantitatively analyze and map sedimentary lithofacies. The observed radiance spectra can be reduced to 'apparent reflectance' spectra by topographic and reflectance characterization of several field sites within the image. These apparent reflectance spectra correspond to the true reflectance at each pixel, multiplied by an unknown illumination factor (ranging in value from zero to one). The spatial abundance patterns of spectrally defined lithofacies and the unknown illumination factors can be simultaneously derived using constrained linear spectral unmixing methods. Estimates of the minimum uncertainty in the final results (due to noise, instrument resolutions, degree of illumination and mixing systematics) can be made by forward and inverse modeling. Specific facies studies in the Rattlesnake Hills region of Wyoming illustrate the successful application of these methods.

Boardmann, Joe W.↗
DOE OSTI2015

The hierarchy solution to the LHC inverse problem

Supersymmetric (SUSY) models, even those described by relatively few parameters, generically allow many possible SUSY particle (sparticle) mass hierarchies. As the sparticle mass hierarchy determines, to a great extent, the collider phenomenology of a model, the enumeration of these hierarchies is of the utmost importance. We therefore provide a readily generalizable procedure for determining the number of sparticle mass hierarchies in a given SUSY model. As an application, we analyze the gravity-mediated SUSY breaking scenario with various combinations of GUT-scale boundary conditions involving different levels of universality among the gaugino and scalar masses. For each of the eight considered models, we provide the complete list of forbidden hierarchies in a compact form. Lastly, our main result is that the complete (typically rather large) set of forbidden hierarchies among the eight sparticles considered in this analysis can be fully specified by just a few forbidden relations involving much smaller subsets of sparticles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Hejre, we introduce physics-informed neural networks – neural networks that are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations. In this work, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct types of algorithms, namely continuous time and discrete time models. The first type of models forms a new family of data-efficient spatio-temporal function approximators, while the latter type allows the use of arbitrarily accurate implicit Runge–Kutta time stepping schemes with unlimited number of stages. Moreover, the effectiveness of the proposed framework is demonstrated through a collection of classical problems in fluids, quantum mechanics, reaction–diffusion systems, and the propagation of nonlinear shallow-water waves.

97 MATHEMATICS AND COMPUTING↗