A metamodeling approach for approximation of multivariate, stochastic and dynamic simulations

This thesis describes the implementation of metamodeling approaches as a solution to approximate multivariate, stochastic and dynamic simulations. In the area of statistics, metamodeling (or “model of a model”) refers to the scenario where an empirical model is build based on simulated data. In this thesis, this idea is exploited by using pre-recorded dynamic simulations as a source of simulated dynamic data. Based on this simulated dynamic data, an empirical model is trained to map the dynamic evolution of the system from the current discrete time step x(s), to the next discrete time step x(s + 1). Therefore, it is possible to approximate the dynamics of the complex dynamic simulation, by iteratively applying the trained empirical model. The rationale in creating such approximate dynamic representation is that the empirical models / metamodels are much more affordable to compute than the original dynamic simulation, while having an acceptable prediction error.;The successful implementation of metamodeling approaches, as approximations of complex dynamic simulations, requires understanding of the propagation of error during the iterative process. Prediction errors made by the empirical model at earlier times of the iterative process propagate into future predictions of the model. The propagation of error means that the trained empirical model will deviate from the expensive dynamic simulation because of its own errors. Based on this idea, Gaussian process model is chosen as the metamodeling approach for the approximation of expensive dynamic simulations in this thesis. This empirical model was selected not only for its flexibility and error estimation properties, but also because it can illustrate relevant issues to be considered if other metamodeling approaches were used for this purpose.;The implementation of Gaussian process models for approximating expensive dynamic simulations begins by understanding and exploring the effects of stochastic observations in this empirical model. It was found that Gaussian process models have a noise limit at which the model is still capable of identifying the local correlation in the residuals, from the stochastics observations. This noise level limit is defined as a signal-to-noise ratio of 1 × 10 1. If the signal-to-noise ratio in the observations is below this number, the identification of local correlation decreases. Also, a methodology is proposed and developed to characterize the error estimation properties of a Gaussian process model. This methodology is later used to quantify the propagation of error in dynamics and then expanded to include multivariate systems. Then, the Gaussian process model is implemented as an iterative mapping function to describe the dynamics of a one-dimensional state with stochastic observations. The results shows how it is possible to track the propagated error during the dynamic prediction by accounting for the input uncertainty in the traditional GPM prediction distribution.;Then, the dynamic implementation of Gaussian process models moves towards multidimensional, stochastic and dynamic systems. Using a well-studied dynamic system in chemical engineering, it was possible to use a multivariate Gaussian process model (cokriging) as an iterative mapping function for the prediction of multivariate dynamic systems. Also, it was shown that Gaussian process models are a good choice to describe the dynamics of systems with stable steady states, thanks to the data density around the steady states. Finally, Gaussian process modeling is implemented as an approximate model to describe the growth of platinum nanoparticles on a carbon nanotube surface. With this elaborate and complex dynamic system, other metamodeling approaches were explored for use can be used as approximate models. In conclusion, the implementation of metamodeling approaches for approximating expensive stochastic dynamic simulations is possible, but it may required of specific statistical tools tailored for the identification of dynamic characteristics in the simulated dynamic data. xx.