Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies

Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies

by Paul G. Constantine

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Overview

Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies by Paul G. Constantine

Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. Thorough parameter studies are, however, challenging, if not impossible, when the simulation is expensive and the model has several inputs. To enable studies in these instances, the engineer may attempt to reduce the dimension of the model's input parameter space. Active subspaces are an emerging set of dimension reduction tools that identify important directions in the parameter space. This book describes techniques for discovering a model's active subspace and proposes methods for exploiting the reduced dimension to enable otherwise infeasible parameter studies. Readers will find new ideas for dimension reduction, easy-to-implement algorithms, and several examples of active subspaces in action. This book is intended for researchers and graduate students in computational science, applied mathematics, statistics, and engineering.

Product Details

ISBN-13: 9781611973853
Publisher: SIAM
Publication date: 08/06/2015
Pages: 110
Product dimensions: 6.85(w) x 9.72(h) x 0.31(d)

About the Author

Paul G. Constantine is the Ben L. Fryrear Assistant Professor of Applied Mathematics and Statistics at Colorado School of Mines. He received his PhD from Stanford's Institute for Computational and Mathematical Engineering and spent two years as the von Neumann Fellow at the Sandia National Laboratories' Computer Science Research Institute. His research interests include uncertainty quantification and dimension reduction for large-scale computer simulations.

Table of Contents

Preface; 1. Quick start; 2. Parameterized models in physics and engineering; 3. Discover the active subspace; 4. Exploit the active subspace; 5. Active subspaces in action; 6. Summary and future directions; Bibliography; Index.

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