Developing Surrogate Models via Computer Based Experiments

Abstract

In recent years, advances in mathematical modeling techniques, algorithms for solving mathematical equations and computational power have all combined to make the study of complex phenomenon with large number of inputs possible, which could otherwise have been unattainable with physical experiments. Particularly excellent computational tools for models on the small scale have opened a new avenue for replacing physical experiments by computational experiments. Often, it is physical/chemical properties that are the target, because they are used in a multitude of models. But since the computational experiments are often of very large scale and high complexity, they require significant computational resources, not least of which is time. Hence, a direct coupling of the codes is not feasible and one has to take refuge in simpler models that are approximating the behaviour of the complex model, called the surrogate models. Naturally the objective is to generate surrogate models that approximate the complex behaviour as well as possible within a given domain. But since computational experiments are not contaminated with stochastic noise, classical design of experiment methods like blocking, randomization and replication are irrelevant (Fang et al., 2005) - the gap is all due to lack of fit. So the maximum acceptable gap in a given domain is usually the essential measure that the application of the surrogate model defines. The goal is clear, one aims at computationally cheap approximations that are sufficiently good as defined by the application. Surrogate models are commonly used in multiscale simulations for bridging the gap between the finer and the coarser scales. We discuss the approach on an illustrative example where the Redlich-Kwong equation of state is approximated by linear surrogate models.