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1st Edition

Advances in High-Order Sensitivity Analysis

By Dan Gabriel Cacuci Copyright 2026

300 Pages

by Chapman & Hall

300 Pages

by Chapman & Hall

300 Pages

by Chapman & Hall

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Description

The high-order sensitivities of model responses with respect to model parameters are notoriously difficult to compute for large-scale models involving many parameters. The neglect of higher-order response sensitivities leads to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis, and higher-order) of the model response’s distribution in the phase space of model... Read more

Table of Contents

Chapter 1. Motivation for Computing High-Order Sensitivities of Model Responses to Model Parameters

1.1. Introduction

1.2. Mathematical Definition of High-Order Response Sensitivities with Respect to Feature Functions of Parameters

1.3. Use of Sensitivities in High-Order Uncertainty Quantification

1.4. High-Order Predictive Modeling: Main Features of the Fourth-Order 4^th-BERRU-PM Methodology

1.5. Illustrative High-Order Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling for the PERP OECD/NEA/ICSBEP Reactor Physics Benchmark

1.5.1. Computational Modeling of the PERP Reactor Physics Benchmark

1.5.2. Computation of the Largest High-Order Sensitivities of the PERP Leakage Response with respect to PERP Parameters

1.5.3. High-Order Uncertainty Quantification

1.5.4. Fourth-Order BERRU (Best Estimate Results with Reduced Uncertainties) Predictive Modeling Applied to the PERP Benchmark

1.6. Chapter Summary

Chapter 2. The 1^st-FASAM-N Methodology for Nonlinear Systems

2.1. Introduction

2.2. Mathematical Modeling of a Generic Nonlinear System Comprising Functions (“Features”) of Uncertain Parameters and Boundaries

2.3. Introducing the 1^st-FASAM-N: First-Order Function/Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems

2.3.1. Comparison Between 1^st-FASAM-N and 1^st-CASAM-N

2.4. Illustrative Application of the 1^st-FASAM-N to a Paradigm Particle Transport Model

2.4.1. Application of the 1^st-CASAM-N to Compute First-Order Response Sensitivities Directly with Respect to Model Parameters

2.4.2. Most Efficient Alternative Procedure: Applying the 1^st-FASAM-N to Compute First-Order Response Sensitivities to Functions/Features of Model Parameters

2.5. Chapter Summary

Chapter 3. The 2^nd-FASAM-N Methodology for Nonlinear Systems

3.1. Introduction

3.2. Mathematical Framework of the 2^nd-FASAM-N Methodology

3.2.1. Similarities and Differences Between the 2^nd-FASAM-N and the 2^nd-CASAM-N

3.3. Applying the 2^nd-FASAM-N to Obtain the Second-Order Response Sensitivities to Functions/Features of Parameters for the Paradigm Particle Transport Model Considered in Chapter 2

3.3.1. Applying the 2^nd-FASAM-N to Compute the 2^nd-Order Response Sensitivities Stemming from the 1^st-Order Sensitivity

3.3.2. Applying the 2^nd-FASAM-N to Compute the 2^nd-Order Response Sensitivities Stemming from the 1^st-Order Sensitivity

3.3.3. Applying the 2^nd-FASAM-N to Compute the 2^nd-Order Response Sensitivities Stemming from the 1^st-Order Sensitivity

3.3.4. Applying the 2^nd-FASAM-N to Compute the 2^nd-Order Response Sensitivities Stemming from the 1^st-Order Sensitivity

3.3.5. Applying the 2^nd-FASAM-N to Compute the 2^nd-Order Response Sensitivities Stemming from the 1^st-Order Sensitivity

3.3.6. Comparing Computational Efficiencies: the 2^nd-FASAM-N versus the 2^nd-CASAM-N

3.4. Chapter Summary

Chapter 4. The Mathematical Framework of the n^th-Order Feature/Function Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n^th-FASAM-N)

4.1. Introduction

4.2. The n^th-Order Feature/Function Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (n^th-FASAM-N)

4.3. The Particular Form of the n^th-FASAM-N Framework for

4.4. Mathematical Framework of the (n+1)^th-FASAM-N Methodology

4.5. Chapter Summary

Chapter 5. Illustrative Application of the n^th-FASAM-N Methodology to the Nordheim-Fuchs Reactor Safety Model

5.1. Introduction

5.2. The Nordheim-Fuchs Phenomenological Reactor Dynamics/Safety Model

5.3. Computation of First-Order Sensitivities of the Model Response to Model Parameters: Application of the 1^st-CASAM-N Versus the 1^st-FASAM-N

5.3.1. Application of the 1^st-CASAM-N to Obtain the First-Order Sensitivities of the Response Directly with Respect to the Model Parameters

5.3.2. Application of the 1^st-FASAM-N to Obtain the First-Order Sensitivities of the Response with Respect to the Features and Model Parameters

5.3.3. Comparative Discussion: Applying the 1^st-CASAM-N versus the 1^st-FASAM-N for Computing the First-Order Response Sensitivities to Model Parameters

5.4. Computation of the Second-Order Response Sensitivities with Respect to Model Parameters: Applying the 2^nd-FASAM-N Versus the 2^nd-CASAM-N

5.4.1. Computation of Second-Order Sensitivities Using the 2^nd-FASAM-N

5.4.2. Computation of Second-Order Sensitivities Using the 2^nd-CASAM-N

5.4.3. Computational Advantages of Using the 2^nd-FASAM-N Versus the 2^nd-CASAM-N

5.5. Computation of the Third-Order Response Sensitivities with Respect to Model Parameters: Applying the 3^rd-FASAM-N Versus the 3^rd-CASAM-N

5.5.1. Computation of Third-Order Sensitivities Using the 3^rd-FASAM-N

5.5.2. Computation of Third-Order Sensitivities Using the 3^rd-CASAM-N

5.6. Chapter Summary

Chapter 6. The nth-Order Features Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-FASAM-L)

6.1. Introduction

6.2. Mathematical Modeling of Response-Coupled Linear Forward and Adjoint Systems

6.3. The First-Order Function/Feature Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward and Adjoint Linear Systems (1^st-FASAM-L)

6.4. The Second-Order Function/Feature Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward and Adjoint Linear Systems (2^nd-FASAM-L)

6.5. The n^th-Order Feature Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward and Adjoint Linear Systems (n^th-FASAM-L)

6.6. Chapter Summary

Chapter 7. Illustrative Application of the n^th-FASAM-L

7.1. Introduction

7.2. Contributon-Flux Response in a Paradigm Neutron Slowing Down Model

7.3. First-Order Adjoint Sensitivity Analysis of the Contributon-Flux Response

7.3.1. Application of the 1^st-FASAM-L Methodology

7.3.2. Application of the 1^st-CASAM-L Methodology

7.4. Second-Order Adjoint Sensitivity Analysis of the Contributon-Flux Response

7.4.1. Application of the 2^nd-FASAM-L Methodology

7.4.2. Application of the 2^nd-CASAM-L Methodology

7.4.3. Comparison: 2^nd-FASAM-L versus 2^nd-CASAM-L

7.5. Third-Order Adjoint Sensitivity Analysis of the Contributon-Flux Response

7.5.1. Application of the 3^rd-FASAM-L Methodology to Compute the 3^rd-Order Sensitivities Stemming from

7.5.2. Application of the 3^rd-FASAM-L Methodology to Compute the 3^rd-Order Sensitivities Stemming from

7.6. Chapter Summary

Author(s)

Biography

Dan Gabriel Cacuci is a Distinguished Professor Emeritus in the Department of Mechanical Engineering at the University of South Carolina and the Karlsruhe Institute of Technology, Germany. He received his PhD in applied physics, mechanical, and nuclear engineering from Columbia University, New York City. He is also the recipient of many awards, including four honorary doctorates, Germany’s Humboldt Preis, the Ernest Orlando Lawrence Memorial Award from the U.S. Department of Energy, and the Arthur Holly Compton, Eugene P. Wigner, and Glenn Seaborg Awards from the American Nuclear Society.

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