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Active Subspaces | An emerging set of dimension reduction tools

What are Active Subspaces? Scientists and engineers use computer models to study input/output relationships in complex physical systems. But thorough parameter studies are challenging—if not impossible—when the simulation is expensive and the model has several inputs. To enable such studies, the engineer may attempt to reduce the dimension of the model’s input space. Emerging ideas for Dimension Reduction in Parameter Studies. By Paul G. Constantine. Website by Josh Shayne Design.

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Active Subspaces | An emerging set of dimension reduction tools | activesubspaces.org Reviews
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What are Active Subspaces? Scientists and engineers use computer models to study input/output relationships in complex physical systems. But thorough parameter studies are challenging—if not impossible—when the simulation is expensive and the model has several inputs. To enable such studies, the engineer may attempt to reduce the dimension of the model’s input space. Emerging ideas for Dimension Reduction in Parameter Studies. By Paul G. Constantine. Website by Josh Shayne Design.
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Active Subspaces | An emerging set of dimension reduction tools | activesubspaces.org Reviews

https://activesubspaces.org

What are Active Subspaces? Scientists and engineers use computer models to study input/output relationships in complex physical systems. But thorough parameter studies are challenging—if not impossible—when the simulation is expensive and the model has several inputs. To enable such studies, the engineer may attempt to reduce the dimension of the model’s input space. Emerging ideas for Dimension Reduction in Parameter Studies. By Paul G. Constantine. Website by Josh Shayne Design.

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Applications | Active Subspaces

http://activesubspaces.org/applications

The HyShotII scramjet model has seven inputs characterizing the inflow conditions. Using active subspaces, we discovered a one-dimensional parameterization that enabled thorough uncertainty quantification studies for the complex, multiphysics simulation. Integrated hydrologic models couple subsurface flow models with land models that characterize the interface between the subsurface and the atmosphere. These models contain several parameters that control the characterization. And these parameters...

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FAQ | Active Subspaces

http://activesubspaces.org/faq

What do I need active subspaces for? How is active subspaces different from principal component analysis? How many samples of the gradient do I need to estimate the active subspace? In our paper Computing active subspaces. We analyze a Monte Carlo method for estimating the eigenvectors. We use nonasymptotic random matrix theory—specifically, some matrix concentration inequalities—developed by Alex Gittens and Joel Tropp to show that the number of samples needed to estimate the k. Active subspaces are der...

3

People | Active Subspaces

http://activesubspaces.org/people

Department of Applied Mathematics and Statistics. Colorado School of Mines. Department of Aerospace Engineering and Engineering Mechanics. Insitute for Computational Engineering and Sciences. The University of Texas at Austin. Department of Aeronautics and Astronautics. Massachusetts Institute of Technology. Department of Aeronautics and Astronautics. Massachusetts Institute of Technology. Colorado School of Mines. Jen Jefferson, Colorado School of Mines. Carson Kent, Stanford University.

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Active Subspaces | An emerging set of dimension reduction tools

What are Active Subspaces? Scientists and engineers use computer models to study input/output relationships in complex physical systems. But thorough parameter studies are challenging—if not impossible—when the simulation is expensive and the model has several inputs. To enable such studies, the engineer may attempt to reduce the dimension of the model’s input space. Emerging ideas for Dimension Reduction in Parameter Studies. By Paul G. Constantine. Website by Josh Shayne Design.

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