Titlebook: Uncertainty Quantification and Predictive Computational Science; A Foundation for Phy Ryan G. McClarren Textbook 2018 Springer Nature Switz

Forage饲料

Local Sensitivity Analysis Based on Derivative Approximationsepends on most strongly. Chapter explores using derivatives as local indicators of sensitivity based on finite difference approximations of first and second-order Taylor expansions. The error in the estimates due to finite differences is discussed, and the complex step approximation is offered as an

xanthelasma

Regression Approximations to Estimate Sensitivities QoI at a nominal point using a least-squares (regression) formulation. This naive approach requires more QoI evaluations than one-sided finite differences as described in the previous chapter. Section 5.2 introduces a regularization term into the least-squares minimization problem, allowing for use

Albinism

Adjoint-Based Local Sensitivity Analysisduces the adjoint operator and demonstrates that for a somewhat general class of QoIs, a QoI can be written as an inner product of the adjoint equations. Then using manipulations involving the definition of the adjoint we arrive at a general formula for the sensitivity to a given QoI to any paramete

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伪书

Reliability Methods for Estimating the Probability of Failurewith the definition of the reliability and the simple first-order second-moment method, which relies heavily on a host of assumptions about the underlying QoI. Then the advanced first-order second-moment method is presented and applied to several problems.

懒鬼才会衰弱

Stochastic Projection and Collocation (polynomial chaos methods) and computational realizations of this using quadrature, collocation, and Galerkin projection. Sparse quadratures are also discussed to evaluate multiple dimensional integrals. The methods are applied to several PDEs including the Poisson’s equation and the Black-Scholes

自爱

Gaussian Process Emulators and Surrogate Models linear regression and show that by using the kernel trick, we can derive a regression model that has an infinite number of basis functions. The resulting Gaussian process models are then used to model a variety of functions, including real simulation data.

laceration

Predictive Models Informed by Simulation, Measurement, and Surrogates experimental data to fix parameters in a simulation. To do this properly, we require Markov Chain Monte Carlo (MCMC) sampling, and this method is discussed in Sect. 11.2. Section 11.3 using MCMC to estimate calibration parameters. The formalism of Kennedy and O’Hagan is then used to introduce a dis

ONYM

狗窝

Textbook 2018icting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences...Constructing sophisticated techniques for prediction from basic building bl