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Adaptive approaches in metamodel-based reliability analysis: A review

Global sensitivity metrics from active subspaces

Random forests for global sensitivity analysis: A selective review

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COVID-19: Development of a robust mathematical model and simulation package with consideration for ageing population and time delay for control action and resusceptibility

Structural reliability analysis based on ensemble learning of surrogate models

Sparse polynomial chaos expansions via compressed sensing and D-optimal design

Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost; commonly used sensitivity metrics include Sobol' total sensitivity indices and derivative-based global sensitivity measures. Active subspaces are an emerging set of tools for identifying important directions in a model's input parameter space; these directions can be exploited to reduce the model's dimension enabling otherwise infeasible parameter studies. In this paper, we develop global sensitivity metrics called activity scores from the active subspace, which yield insight into the important model parameters. We mathematically relate the activity scores to established sensitivity metrics, and we discuss computational methods to estimate the activity scores. We show two numerical examples with algebraic functions taken from simplified engineering models. For each model, we analyze the active subspace and discuss how to exploit the low-dimensional structure. We then show that input rankings produced by the activity scores are consistent with rankings produced by the standard metrics.

A Modified SEIR Model for the Spread of Ebola in Western Africa and Metrics for Resource Allocation

Active subspaces are part of an emerging set of tools for discovering and exploiting lowdimensional structure in a function of several variables (Constantine 2015; Constantine, Dow, and Wang 2014). The active subspace for a given function is the span of a set of important directions in the function’s domain, where importance is defined by the eigenvalues of a symmetric, positive semidefinite matrix derived from the function’s partial derivatives. Perturbing the inputs within the active subspace changes the output more, on average, than perturbing the inputs orthogonally to the active subspace. The functions of interest arise in complex computer simulation models in science and engineering, where the inputs are the model’s physical parameters and the output is the scientific or engineering quantity of interest. Identifying an active subspace in a given model enables one to reduce the input dimension for essential parameter studies—such as optimization or uncertainty quantification. When the simulation model is computationally expensive, this dimension reduction may enable otherwise infeasible parameter studies.

/pdf/python-active-subspaces-utility-library-1gdkfxnah4.pdf

Paul Diaz

Papers

Global sensitivity metrics from active subspaces

Sparse polynomial chaos expansions via compressed sensing and D-optimal design

Global sensitivity metrics from active subspaces

A Modified SEIR Model for the Spread of Ebola in Western Africa and Metrics for Resource Allocation

Python Active-subspaces Utility Library