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

TL;DR

This paper introduces RMFGP, a novel rotated multi-fidelity Gaussian process framework with dimension reduction and active learning, enabling efficient high-dimensional uncertainty quantification with limited data, outperforming existing methods.

Contribution

It develops a new dimension reduction approach based on rotated Gaussian processes combined with Bayesian active learning for high-dimensional problems.

Findings

RMFGP outperforms traditional models in four numerical examples.

The method effectively handles high-dimensional problems with limited data.

Uncertainty propagation analysis confirms the model's accuracy.

Abstract

Multi-fidelity modelling arises in many situations in computational science and engineering world. It enables accurate inference even when only a small set of accurate data is available. Those data often come from a high-fidelity model, which is computationally expensive. By combining the realizations of the high-fidelity model with one or more low-fidelity models, the multi-fidelity method can make accurate predictions of quantities of interest. This paper proposes a new dimension reduction framework based on rotated multi-fidelity Gaussian process regression and a Bayesian active learning scheme when the available precise observations are insufficient. By drawing samples from the trained rotated multi-fidelity model, the so-called supervised dimension reduction problems can be solved following the idea of the sliced average variance estimation (SAVE) method combined with a Gaussian process regression dimension reduction technique. This general framework we develop can effectively solve high-dimensional problems while the data are insufficient for applying traditional dimension reduction methods. Moreover, a more accurate surrogate Gaussian process model of the original problem can be obtained based on our trained model. The effectiveness of the proposed rotated multi-fidelity Gaussian process(RMFGP) model is demonstrated in four numerical examples. The results show that our method has better performance in all cases and uncertainty propagation analysis is performed for last two cases involving stochastic partial differential equations.