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4 - Third-Order Sensitivity Analysis, Uncertainty Quantification, Data Assimilation, Forward and Inverse Predictive Modelling for Large-Scale Systems

from Part I - Introduction

Published online by Cambridge University Press:  20 June 2023

By
Dan Gabriel Cacuci
Edited by
Alik Ismail-Zadeh ,
Fabio Castelli ,
Dylan Jones  and
Sabrina Sanchez
Alik Ismail-Zadeh
Affiliation:
Karlsruhe Institute of Technology, Germany
Fabio Castelli
Affiliation:
Università degli Studi, Florence
Dylan Jones
Affiliation:
University of Toronto
Sabrina Sanchez
Affiliation:
Max Planck Institute for Solar System Research, Germany
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Summary

Abstract: This chapter presents a third-order predictive modelling methodology which aims at obtaining best-estimate results with reduced uncertainties (acronym: 3rd-BERRU-PM) for applications to large-scale models comprising many parameters. The building blocks of the 3rd-BERRU-PM methodology include quantification of third-order moments of the response distribution in the parameter space using third-order adjoint sensitivity analysis (which overcomes the curse of dimensionality), assimilation of experimental data, model calibration, and posterior prediction of best-estimate model responses and parameters with reduced best-estimate variances/covariances for the predicted responses and parameters. Applications of these concepts to an inverse radiation transmission problem, to an oscillatory dynamical model, and to a large-scale computational model involving 21,976 uncertain parameters, respectively, are also presented, thus illustrating the actual computation and impacts of the first-, second-, and third-order response sensitivities to parameters on the expectation, variance, and skewness of the respective model responses.

Keywords

adjoint sensitivity systembest-estimate parameterbest-estimate responsecurse of dimensionalityexpectationforward predictive modelinghigh-order sensitivityinverse predictive modelingreduced uncertaintyvariance
Type
Chapter
Information
Applications of Data Assimilation and Inverse Problems in the Earth Sciences , pp. 49 - 76
Publisher: Cambridge University Press
Print publication year: 2023

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