Gaussian Process Emulation for High-Dimensional Coupled Systems

Abstract

Complex coupled multiphysics simulations are ubiquitous in science and engineering. Evaluating these numerical simulators is often costly which limits our ability to run them sufficiently often for forward uncertainty quantification. Furthermore outputs are generally not scalar quantities but depend on space and/or time. Gaussian process emulators are statistical surrogates which can approximate the output of the complex computer models at untested inputs quickly while also providing uncertainty information about the accuracy of evaluating the emulator rather than the full physical model. GP emulators were originally developed in the context of scalar output from a single physical model but have since been extended to vector-valued quantities of interest (parallel partial emulators) and to coupled physics by connecting two independent emulators, one for each type of physics (linked emulation). The parallel partial linked GP emulator (PPLE) developed in this work combines the efficiency of a shared correlation structure with the accuracy of linked emulators to produce a new tool for emulating compositions of functions with vector-valued output. The PPLE applied to two numerical experiments out-performs direct emulation of the output composite function producing results with smaller average prediction error and variance.