MULTI-PRED: A Software Module for Predictive Modeling of Coupled Multi-Physics Systems

Cacuci, Dan Gabriel; Fang, Ruixian; Badea, Madalina C.

doi:10.1080/00295639.2018.1451675

Cited by 3 publications

(9 citation statements)

References 17 publications

(16 reference statements)

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“…This work was subsequently extended by Cacuci and Ionescu-Bujor [19], which presented analytical formulas for predicted mean values and covariance matrices, for both predicted model parameters and responses, which have generalized the previous results presented in data assimilation procedures for geophysical sciences and linear Bayesian models. Other applications to nuclear energy systems are presented in [20][21][22][23][24][25][26][27].…”

Section: Nd/3rd-order Best-estimated Results With Reduced Uncertaintmentioning

confidence: 99%

“…is defined on the phase-space boundary x ∈ ∂Ω x . (iii) Identify the first term on the right-side of Equation (34) with the indirect-effect term defined in Equation (27) by requiring that the following system of equations be satisfied for…”

Section: The Second-level Adjoint System (2nd-lass) For Computing Examentioning

confidence: 99%

“…None of these 2nd-and 3rd-order sensitivities appear in the works previous to this work. Consequently, the 2nd/3rd-BERRU-PM formalism comprises, as particular cases, the previously published formulas used in Kalman filters, Bayesian linear statistics [10], data adjustment [13][14][15][16][17], data assimilation [8,9] and predictive modeling [7,[18][19][20][21][22][23][24][25][26][27].…”

Section: Data Consistency Indicatormentioning

confidence: 99%

See 2 more Smart Citations

Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantification and Predictive Modeling

Cacuci

2019

Energies

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This work presents the Third-Order Adjoint Sensitivity Analysis Methodology (3rd-ASAM) for response-coupled forward and adjoint linear systems. The 3rd-ASAM enables the efficient computation of the exact expressions of the 3rd-order functional derivatives (“sensitivities”) of a general system response, which depends on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward and adjoint systems. Such responses are often encountered when representing mathematically detector responses and reaction rates in reactor physics problems. The 3rd-ASAM extends the 2nd-ASAM in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling. This work also presents new formulas that incorporate the contributions of the 3rd-order sensitivities into the expressions of the first four cumulants of the response distribution in the phase-space of model parameters. Using these newly developed formulas, this work also presents a new mathematical formalism, called the 2nd/3rd-BERRU-PM “Second/Third-Order Best-Estimated Results with Reduced Uncertainties Predictive Modeling”) formalism, which combines experimental and computational information in the joint phase-space of responses and model parameters, including not only the 1st-order response sensitivities, but also the complete hessian matrix of 2nd-order second-sensitivities and also the 3rd-order sensitivities, all computed using the 3rd-ASAM. The 2nd/3rd-BERRU-PM uses the maximum entropy principle to eliminate the need for introducing and “minimizing” a user-chosen “cost functional quantifying the discrepancies between measurements and computations,” thus yielding results that are free of subjective user-interferences while generalizing and significantly extending the 4D-VAR data assimilation procedures. Incorporating correlations, including those between the imprecisely known model parameters and computed model responses, the 2nd/3rd-BERRU-PM also provides a quantitative metric, constructed from sensitivity and covariance matrices, for determining the degree of agreement among the various computational and experimental data while eliminating discrepant information. The mathematical framework of the 2nd/3rd-BERRU-PM formalism requires the inversion of a single matrix of size Nr Nr, where Nr denotes the number of considered responses. In the overwhelming majority of practical situations, the number of responses is much less than the number of model parameters. Thus, the 2nd-BERRU-PM methodology overcomes the curse of dimensionality which affects the inversion of hessian matrices in the parameter space.

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Section: Nd/3rd-order Best-estimated Results With Reduced Uncertaintmentioning

confidence: 99%

Section: The Second-level Adjoint System (2nd-lass) For Computing Examentioning

confidence: 99%

Section: Data Consistency Indicatormentioning

confidence: 99%

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Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantification and Predictive Modeling

Cacuci

2019

Energies

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“…Table 5. 4 Comparison between the nominal cross sections and the mean of the sampled cross section distributions. .…”

Section: List Of Tablesmentioning

confidence: 99%

“…The sensitivities given by Favorite are also defined for the fission spectrum as a function of incident and emergent neutron energies. 4 The sensitivities given in Table 2.1 are defined in terms of inner products between forward and adjoint angular fluxes as well as between their Legendre polynomial expansion moments for a onedimensional geometry. The scatter cross section is also given in terms of its Legendre polynomial expansion moments.…”

Section: Multigroup Approximation and Legendre Polynomial Expansion Amentioning

confidence: 99%

Application of Neutron Multiplicity Counting Experiments to Optimal Cross-Section Adjustments

Clark

Mattingly

Favorite

2020

Nuclear Science and Engineering

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CLARK, ALEXANDER RICH. Application of Neutron Multiplicity Counting Experiments to Optimal Cross Section Adjustments. (Under the direction of John Mattingly.) This dissertation presents the first application of model calibration to neutron multiplicity counting (NMC) experiments for cross section optimization that utilizes adjoint-based sensitivity analysis (SA) and first-order uncertainty quantification (UQ). We summarize previous work on SA applied to NMC and describe notable additions. We give the procedure for first-order UQ and Bayesian-inference-based parameter estimation (PE). We then discuss model calibration applied to NMC of a 4.5-kg sphere of weapons-grade, alpha-phase plutonium metal with a neutron multiplicity counter. For bare and polyethylene-reflected configurations of the plutonium sphere, we discuss the sensitivity of the first-and second-moment detector responses (i.e. first and second moments of the NMC distribution, respectively) to the cross sections. We describe the sources of uncertainty in the measured and simulated responses. Specifically, uncertainty in the measured responses is due to both random and systematic sources of uncertainty. Uncertainty in the simulated responses is due to cross section covariances. We describe in detail the adjustment to the cross sections and cross section covariances due to the optimization. Due to the contribution of systematic uncertainties to the measured response uncertainties, the adjustment to the cross sections is similar in trend but larger in magnitude compared to that recommended by previous work. We compare the measured responses to responses simulated with nominal and optimized cross sections, demonstrating that the best-estimate cross sections produce simulations of NMC experiments that are more accurate with reduced uncertainty. We verify that the response variance due to the cross sections computed with sampling-based uncertainty quantification (UQ) is well-approximated by that estimated with first-order UQ.

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Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework

Cacuci

2021

Energies

Self Cite

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The most general quantities of interest (called “responses”) produced by the computational model of a linear physical system can depend on both the forward and adjoint state functions that describe the respective system. This work presents the Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (4th-CASAM) for linear systems, which enables the efficient computation of the exact expressions of the 1st-, 2nd-, 3rd- and 4th-order sensitivities of a generic system response, which can depend on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward/adjoint systems. Among the best known such system responses are various Lagrangians, including the Schwinger and Roussopoulos functionals, for analyzing ratios of reaction rates, the Rayleigh quotient for analyzing eigenvalues and/or separation constants, etc., which require the simultaneous consideration of both the forward and adjoint systems when computing them and/or their sensitivities (i.e., functional derivatives) with respect to the model parameters. Evidently, such responses encompass, as particular cases, responses that may depend just on the forward or just on the adjoint state functions pertaining to the linear system under consideration. This work also compares the CPU-times needed by the 4th-CASAM versus other deterministic methods (e.g., finite-difference schemes) for computing response sensitivities These comparisons underscore the fact that the 4th-CASAM is the only practically implementable methodology for obtaining and subsequently computing the exact expressions (i.e., free of methodologically-introduced approximations) of the 1st-, 2nd, 3rd- and 4th-order sensitivities (i.e., functional derivatives) of responses to system parameters, for coupled forward/adjoint linear systems. By enabling the practical computation of any and all of the 1st-, 2nd, 3rd- and 4th-order response sensitivities to model parameters, the 4th-CASAM makes it possible to compare the relative values of the sensitivities of various order, in order to assess which sensitivities are important and which may actually be neglected, thus enabling future investigations of the convergence of the (multivariate) Taylor series expansion of the response in terms of parameter variations, as well as investigating the range of validity of other important quantities (e.g., response variances/covariance, skewness, kurtosis, etc.) that are derived from Taylor-expansion of the response as a function of the model’s parameters. The 4th-CASAM presented in this work provides the basis for significant future advances towards overcoming the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

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MULTI-PRED: A Software Module for Predictive Modeling of Coupled Multi-Physics Systems

Cited by 3 publications

References 17 publications

Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantification and Predictive Modeling

Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantification and Predictive Modeling

Application of Neutron Multiplicity Counting Experiments to Optimal Cross-Section Adjustments

Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework

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