High dimensional model representations

In the chemical sciences, many laboratory experiments, environmental and in dustrial processes, as well as modeling exercises, are characterized by lar ge numbers of input variables. A general objective in such cases is an expl oration of the high-dimensional input variable space as thoroughly as possi ble for its impact on observable system behavior, often with either optimiz ation in mind or simply for achieving a better understanding of the phenome na involved. An important concern when undertaking these explorations is th e number of experiments or modeling excursions necessary to effectively lea rn the system input --> output behavior, which is typically a nonlinear rel ationship. Although simple logic suggests that the number of runs could gro w exponentially with the number of input variables, broadscale evidence ind icates that the required effort often scales far more comfortably. This pap er considers an emerging family of high dimensional model representation co ncepts and techniques capable of dealing with such input --> output problem s in a practical fashion. A summary of the state of the subject is presente d. along with several illustrations from various areas in the chemical scie nces.