An ensemble learning approach to aggregate the output from multiple simulators and measurements

We consider in this paper the problem of aggregating the output from multiple computer simulators (models) and measurements to make inference on a stochastic quantity of interest. Our ensemble learning approach consists in a clustering-Bagging step, followed by a data assimilation step based on Bayesian model averaging or Bayesian model combination. Unsupervised clustering is the first step in the ensemble learning approach and serves the purpose of distinguishing the output from each simulator (or model), and deriving apriori probability map (weights) of the simulators. Clustering is performed on the stochastic output corresponding to the binned input space, where each bin is considered as a dimension. The second step consists in a weighted Bootstrap Aggregation (Bagging), which serves the purpose of weighted aggregation (combination) of the clustered ensemble of outputs from the individual simulators. Finally, when observational training datasets of the quantity of interest become available, the Bayesian Model Averaging (BMA) or Bayesian Mode Combination (BMC) is used to combine the prior aggregated simulations predictions with the assimilated data to update the posterior model probabilities (weights) of each of the proposal models. We demonstrate our approach on the extreme blade deflection of a wind turbine blade