Circuit Analysis Under Process Variations

Probabilistic Assessment of Antarctic Thermomechanical Structure: Impacts on Ice Sheet Stability

“…If it is not practical to calculate all N S values of 𝐴𝐴  𝑖𝑖 , due to computational expense, a subset N U of the overall set of post burn-in models may be used (see Section 4). The relationship between the uncertainty on a physical prediction, 𝐴𝐴 V𝑉 (𝑓𝑓 ( )) , and the uncertainty on the underlying model parameters, 𝐴𝐴 V𝑽 ( ) , is dependent on the sensitivity of 𝐴𝐴 𝐴𝐴( ) to each parameter, 𝐴𝐴 𝑖𝑖 (i.e., the gradient, 𝐴𝐴 𝐴𝐴𝐴𝐴 ( )∕𝐴𝐴𝑖𝑖 ), and the covariance structure of the model, 𝐴𝐴 𝚺𝚺  (Champac & Garcia Gervacio, 2018). In the case of the anelasticity parameterization, 𝐴𝐴 𝐴𝐴( ) and 𝐴𝐴 𝐴𝐴( ) are non-linear functions of V S , complicating the analytical calculation of their expectation value and variance.…”

“…If it is not practical to calculate all N S values of $${\mathcal{F}}^{i}$$, due to computational expense, a subset N U of the overall set of post burn‐in models may be used (see Section 4). The relationship between the uncertainty on a physical prediction, $$\hat{V}(f(\boldsymbol{\mathcal{X}}))$$, and the uncertainty on the underlying model parameters, $$\hat{\boldsymbol{V}}(\boldsymbol{\mathcal{X}})$$, is dependent on the sensitivity of $$f(\boldsymbol{\mathcal{X}})$$ to each parameter, $${\mathcal{X}}_{i}$$ (i.e., the gradient, $$\partial f(\boldsymbol{\mathcal{X}})/\partial {\mathcal{X}}_{i}$$), and the covariance structure of the model, $${\boldsymbol{\Sigma }}^{\boldsymbol{\mathcal{X}}}$$ (Champac & Garcia Gervacio, 2018). In the case of the anelasticity parameterization, $$T(\boldsymbol{\mathcal{X}})$$ and $$\eta (\boldsymbol{\mathcal{X}})$$ are non‐linear functions of V S , complicating the analytical calculation of their expectation value and variance.…”