Revealing the dependence structure of scenario-like inputs in numerical environmental simulations using Gaussian Process regression
Résumé
Model uncertainties (related to the structure/form of the model or to the choice of "appropriate" physical laws) are generally integrated in environmental long running numerical simulators via scenario-like variables. By focusing on Gaussian Processes (GP), we show how different categorical covariance functions (exchangeable, ordinal, group, etc.) can bring valuable insights into the inter-dependencies of these scenarios. Supported by two real case applications (cycloneinduced waves and reservoir modelling), we have proposed a cross-validation approach to select the most appropriate covariance function by finding a trade-off between predictability, explainability, and stability of the covariance coefficients. This approach can be effectively used to support (or contradict) some physical assumptions regarding the scenario-like input. Through comparison to tree-based techniques, we show that GP models can be considered a satisfactory compromise when only a few model runs (~100) are available by presenting a high predictability and a concise and graphical way to map the dependence.
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