A random forest with multi-fidelity Gaussian process leaves for modeling multi-fidelity data with heterogeneity

Modeling multi-fidelity datasets has been widely used recently. High-fidelity data often suffer from scarcity. Low-fidelity models have abundant observations where information from low-fidelity models can be transferred to high-fidelity models. However, the modeling performance for the multi-fidelity models is below par in most cases due to the heterogeneity of the data. Modeling time is also a critical issue for MF datasets due to high dimension of the data. We propose to frame a multi-fidelity Gaussian process model into a random forest framework to incorporate its flexibility and improve the prediction performance when there are a limited amount of high-fidelity data and the data exhibit heterogeneity in the space of interest. Information extracted from the low-fidelity model can be borrowed for the high-fidelity model by capturing cross-level data correlations. The multi-fidelity model is extended to a tree ensemble structure with an efficient partitioning criterion to tackle data heterogeneity. The proposed method is able to provide uncertainty quantification for predicted values. Numerical examples and case studies are conducted to show the efficacy of our method for the heterogeneous behaviors of the responses across the input space.