Multi-Stage Bayesian Surrogates for the Design of Time-Dependent Systems

During the early stages of the design process, designers rarely have accurate models of system behavior, yet the success of their designs depends on understanding the effect of changes in the design parameters on the system response. When models are available, they are often expensive to evaluate and difficult to run, in large part due to the imprecise knowledge available at the beginning of the design process. To circumvent these problems, a common approach proposed in the literature is the use of surrogate models. In this paper, we propose a framework for building surrogate models in multiple stages for time-dependent systems. Because they are built in stages, the surrogate models can respond to changes in constraints and can be fine-turned as design decisions are made. When designers have mathematical models available, they can perform repeated sensitivity analyses, explore trade-offs and perform optimization studies. In this framework, the observed responses are viewed as a set of time-correlated spatial processes. The framework uses optimal sampling techniques to improve the accuracy of the resulting surrogate model while keeping the number of samples to a minimum. A new non-stationary covariance structure is proposed and tested with an example design application. The resulting models are compared with the surrogates obtained with the stationary covariance structure proposed by Romero et al. [1]. The results show increased accuracy using the non-stationary covariance structure due to its superior interpolation capabilities.