Integrated Emulators for Systems of Computer Models
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We generalize the state-of-the-art linked emulator for a system of two computer models under the squared exponential kernel to an integrated emulator for any feed-forward system of multiple computer models, under a variety of kernels (exponential, squared exponential, and two key Matérn kernels) that are essential in advanced applications. The integrated emulator combines Gaussian process emulators of individual computer models, and predicts the global output of the system using a Gaussian distribution with explicit mean and variance. By learning the system structure, our integrated emulator outperforms the composite emulator, which emulates the entire system using only global inputs and outputs. Orders of magnitude prediction improvement can be achieved for moderate-size designs. Furthermore, our analytic expressions allow a fast and efficient design algorithm that allocates different runs to individual computer models based on their heterogeneous functional complexity. This design yields either significant computational gains or orders of magnitude reductions in prediction errors for moderate training sizes. We demonstrate the skills and benefits of the integrated emulator in a series of synthetic experiments and a feed-back coupled fire-detection satellite model.
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