| Abstract
| - In the chemical sciences, many laboratory experiments, environmental and industrial processes, as well asmodeling exercises, are characterized by large numbers of input variables. A general objective in such casesis an exploration of the high-dimensional input variable space as thoroughly as possible for its impact onobservable system behavior, often with either optimization in mind or simply for achieving a betterunderstanding of the phenomena involved. An important concern when undertaking these explorations is thenumber of experiments or modeling excursions necessary to effectively learn the system input → outputbehavior, which is typically a nonlinear relationship. Although simple logic suggests that the number of runscould grow exponentially with the number of input variables, broadscale evidence indicates that the requiredeffort often scales far more comfortably. This paper considers an emerging family of high dimensional modelrepresentation concepts and techniques capable of dealing with such input → output problems in a practicalfashion. A summary of the state of the subject is presented, along with several illustrations from variousareas in the chemical sciences.
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