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Multi-fidelity modelling arises in many situations in computational scienceand engineering world. It enables accurate inference even when only a small setof accurate data is available. Those data often come from a high-fidelitymodel, which is computationally expensive. By combining the realizations of thehigh-fidelity model with one or more low-fidelity models, the multi-fidelitymethod can make accurate predictions of quantities of interest. This paperproposes a new dimension reduction framework based on rotated multi-fidelityGaussian process regression and a Bayesian active learning scheme when theavailable precise observations are insufficient. By drawing samples from thetrained rotated multi-fidelity model, the so-called supervised dimensionreduction problems can be solved following the idea of the sliced averagevariance estimation (SAVE) method combined with a Gaussian process regressiondimension reduction technique. This general framework we develop caneffectively solve high-dimensional problems while the data are insufficient forapplying traditional dimension reduction methods. Moreover, a more accuratesurrogate Gaussian process model of the original problem can be obtained basedon our trained model. The effectiveness of the proposed rotated multi-fidelityGaussian process(RMFGP) model is demonstrated in four numerical examples. Theresults show that our method has better performance in all cases anduncertainty propagation analysis is performed for last two cases involvingstochastic partial differential equations.

RMFGP: Rotated Multi-fidelity Gaussian process with Dimension Reduction for High-dimensional Uncertainty Quantification