Computer Experiments Designed to Explore and Approximate Complex Deterministic Models

Sammanfattning: Computer experiments are widely used to investigate how technical, economic, and ecological systems respond to changes in inputs or driving forces. This thesis is focused on design of computer experiments that can help us better understand the output from complex computer code models. The major part of our work was devoted to experiments involving derivation and application of computationally cheaper surrogate models of a given computer code model. We developed an adaptive sequential design algorithm that efficiently reveals nonlinearities in the model output, and we integrated this algorithm with methods for predicting model outputs at untried inputs. Compared to the methods currently in use, our sequential design has the advantage of not requiring any prior information about the response of the investigated model output to changes in the inputs. Of special interest, we found that our algorithm works satisfactorily even if the curvature of the response surface varies strongly over the input domain. Variance-based sensitivity analysis is a well-established technique to elucidate model outputs, but it can become prohibitively expensive to implement because it requires numerous model runs. Surrogate models can facilitate such analysis, and if our sequential design algorithm is utilized, it can supply useful information about both linear and nonlinear responses to model inputs. Experiments involving repeated runs of a model of the flow of water and nitrogen through a river basin showed that our approach can be applied to extract the essence of complex deterministic models. In addition, our research showed that computationally inexpensive surrogate models offer an ideal basis for interactive decision support tools and learning processes, because they can provide almost immediate responses to user-defined model inputs.