Active Subspaces: Emerging Ideas for Dimension Reduction in Parameter Studies

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. Parameter studies are everywhere in computational science. Complex engineering simulations must run several times with different inputs to effectively study the relationships between inputs and outputs. Studies like optimization, uncertainty quantification, and sensitivity analysis produce sophisticated characterizations of the input/output map. But thorough parameter studies are more difficult when each simulation is expensive and the number of parameters is large. In practice, the engineer may try to limit a study to the most important parameters, which effectively reduces the dimension of the parameter study.