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Thus, the higher order sensitivity would quantify the impact this relationship has on the model output.
For a non-additive model, higher order sensitivity indices, which are responsible for interaction effects among sets of input factors, must be computed.
The higher order sensitivity coefficients in the Taylor series expansion are less commonly computed, and hence the focus of the current work is only on the first-order sensitivities.
However, higher order sensitivity indices are usually not estimated, as in a model with k factors the total number of indices (including the S i s) that should be estimated is as high as 2 k −1.
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Fourier differentiation (FD) provides higher order sensitivities by conducting an FFT analysis of multiple complex variable analyses around a sampling radius in the complex plane.
Assessing different higher order sensitivities effects of different sets of input parameters on model outputs contributes to: quantifying parameters having the highest impact on outputs uncertainties, traversing output design space efficiently, and converging to a higher circuit performance in a reasonable runtime compared to other approaches.
Higher order sensitivities can capture possible parameter interactions.
Here, we focus on three global sensitivity methods: a basic, easily-implemented method of average local sensitivities, and two more complex methods that capture first-order sensitivities, as well as higher order sensitivities, those sensitivities derived from varying more than one parameter.
By applying automatic differentiation to these micromechanics incremental schemes, the first order and high order sensitivities of the effective material properties can be easily computed in the same analysis.
In addition, high-order sensitivity indices were all smaller than 0.01, which indicates that interaction effects of these six factors were practically insignificant.
Some results in higher-order sensitivity analysis using a higher-order adjacent derivative in [22] and a higher-order contingent derivative in [23] of perturbation maps in a parameterized vector optimization were given.
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