Bayesian-validated computer-simulation surrogates for optimization and design: Error estimates and applications

We present a Bayesian-validated surrogate framework which permits economical and reliable integration of large-scale simulations into engineering design and optimization. In the surrogate approach, the large-scale simulation is evoked only to construct and validate a simplified input-output model; this simplified input-output model then serves as a simulation surrogate in subsequent engineering optimization studies. The distinguishing features of our approach are: sequential statistical sampling procedures which permit both efficient adaptive surrogate construction and rigorous ‘probably-approximately-correct’ surrogate validation; and validation-based non-parametric a posteriori error estimates which precisely quantify the effect of surrogate-for-simulation substitution on system predictability and optimality. In this paper we discuss recent improvements and extensions to our construction-validation algorithms and a posteriori error framework, and present several illustrative applications in heat transfer and fluid mechanics.