The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume I: Overcoming the Curse of Dimensionality: Linear Systems

Parameters, independent and dependent variables, and uncertainties affect the results predicted by computational models of physical systems. The functional derivatives of these results are needed for understanding the model, reduced-order modeling, quantifying uncertainties, model validation, prioritizing improvements, data assimilation, and model calibration. This 3-Volume monograph describes a comprehensive adjoint sensitivity analysis methodology that enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems. It includes the treatment of linear systems in their own right, unlike responses for nonlinear systems. Volume 1 presents the mathematical framework, Volume 2 applies it to a reactor physics benchmark, and Volume 3 presents the methodology for nonlinear systems. This methodology overcomes the "curse of dimensionality" in sensitivity and uncertainty analysis, revolutionizing fields that require accurate computation of response sensitivities.

Format: Hardback
Length: 362 pages
Publication date: 20 July 2022
Publisher: Springer Nature Switzerland AG

Computational models of physical systems encompass a combination of parameters and independent and dependent variables. Due to the inherent uncertainties in the physical processes and the experimental procedures used to derive most model parameters, the predictions generated by these models are inherently imprecise. These uncertainties can significantly impact the accuracy of the results.

For various purposes, such as understanding the model, performing reduced-order modeling, quantifying uncertainties, validating the model, prioritizing improvements, data assimilation, model calibration, forward predictive modeling, inverse predictive modeling, and designing and optimizing the system, the functional derivatives (also known as "sensitivities") of the results (also referred to as "responses") produced by mathematical/computational models are crucial.

The author has developed a comprehensive adjoint sensitivity analysis methodology that enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems with numerous model parameters, including the systems uncertain boundaries. This methodology provides a powerful tool for analyzing and understanding the sensitivity of model outcomes to changes in the model parameters and their interactions.

By employing this methodology, researchers and practitioners can gain insights into the importance of different model parameters, identify redundant or unimportant processes, quantify the uncertainties associated with model responses, validate the model's accuracy, prioritize improvements, perform data assimilation and model calibration, and optimize the system for better performance.

In conclusion, the comprehensive adjoint sensitivity analysis methodology presented in this 3-Volume monograph offers a valuable tool for analyzing and understanding the sensitivity of model responses in complex physical systems. It enables researchers and practitioners to make informed decisions based on the analysis of model uncertainties and improve the accuracy and reliability of their predictions.

Weight: 729g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030963637
Edition number: 1st ed. 2022