The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume II: Overcoming the Curse of Dimensionality: Large-Scale Application

The nth-CASAM is an adjoint sensitivity analysis methodology that overcomes the "curse of dimensionality" in sensitivity and uncertainty analysis by computing arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. It is applicable to any model and becomes more efficient with increasing number of model parameters. Volume Two presents a fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark, demonstrating that many 4th-order sensitivities are larger than 3rd-order ones, which are larger than 2nd-order ones, and all of which are larger than 1st-order sensitivities.

Format: Hardback
Length: 463 pages
Publication date: 27 April 2023
Publisher: Springer International Publishing AG

Here is the rephrased text:

Comprehensive Adjoint Sensitivity Analysis Methodology (nth-CASAM)
The nth-CASAM framework, developed by the author, is a groundbreaking methodology that enables the efficient and precise computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. Unlike traditional approaches that rely on exponentially increasing parameter-dimensional spaces, nth-CASAM operates in linearly increasing Hilbert spaces, each with state-function-dimensionality. This innovative approach overcomes the so-called "curse of dimensionality" in sensitivity and uncertainty analysis, making it applicable to a wide range of models.

As the number of model parameters increases, the efficiency of nth-CASAM for computing arbitrarily high-order response sensitivities exponentially grows. This makes it an invaluable tool for practitioners working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems, and predictive modelling.

In this Volume Two, the second of three, the nth-CASAM framework is applied to perform a comprehensive fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark, modeled mathematically by the Boltzmann particle transport equation, involves a staggering 21,976 imprecisely-known parameters. The numerical solution of such a complex system requires extensive large-scale computations.

The sensitivity analysis presented in this volume is the most comprehensive ever conducted in the field of reactor physics. The results, which may seem counterintuitive at first glance, demonstrate that many of the fourth-order sensitivities are significantly larger than expected. This groundbreaking work sheds new light on the complex dynamics and interactions within large-scale systems and has significant implications for safety and reliability analysis.

Overall, the nth-CASAM framework represents a significant advancement in the field of sensitivity analysis, offering a powerful tool for researchers and practitioners to explore the complex dynamics of large-scale systems and improve their understanding and decision-making processes.

Weight: 887g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031196348
Edition number: 1st ed. 2023