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Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies

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by Paul G. Constantine


2015 / x + 100 pages / Softcover / ISBN 978-1-611973-85-3 / List Price $39.00 / SIAM Member Price $27.30 / Order Code SL02

Keywords: active subspaces, dimension reduction, uncertainty quantification, large-scale simulations, computational science


SIREV Book Review

Scientists and engineers use computer simulations to study relationships between a model's input parameters and its outputs. However, thorough parameter studies are 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.

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 Ph.D. 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.

ISBN 9781611973853

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