ADVANCED GAUSSIAN PROCESSES FOR THE SURROGATE MODELLING OF ENERGY SYSTEMS
Résumé
Surrogate models are efficient and accurate approximations of computationally expensive numerical models, derived from the statistical analysis of a limited number of model evaluations. Their primary purpose is to mitigate the computational burden. Surrogates are used for a wide variety of tasks such as sensitivity analysis (identifying the most influential parameters or parameter combinations), model calibration, uncertainty propagation and system optimization. Among other techniques, Gaussian Processes (GP) are especially appealing since they lie on sound theoretical foundations, are known to be flexible, rather accurate and, to some extent, they can be interpreted. This paper investigates to which extent advanced variants of GPs can improved the prediction when an exponentially increasing number of parameter combinations that must be explored. Multi-start strategy for the GP training, alternative objectives for GP training and linear embedding (i.e. considering a linear transformation of the variables) are investigated. Throughout this study, a dataset of 4589 time-dependent simulations of a geothermal absorption cooling system with 17 sizing variables is used. It turns out that none of these strategies can improve the Cross-Validation Root Mean Square Error when compared to standard GP training with Log Marginal Likelihood maximization, GP training with a single deterministic starting point, and no linear embedding. Applying standard GP algorithms and approaches seems sufficient for the surrogate modelling of energy systems, at least for the considered dataset.
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