Hierarchical regression framework for multi-fidelity modeling

Abstract

High-fidelity (HF) samples are accurate but are obtained at high cost, and low-fidelity (LF) samples are widely available but provide rough approximations. Multi-fidelity modeling aims to incorporate massive LF samples with a small amount of HF samples to develop a model for accurately approximating the HF responses to unseen inputs. In this paper, we propose a hierarchical regression framework for multi-fidelity modeling that includes a hierarchical regressor for bi-fidelity modeling and a recursive method for multi-fidelity modeling. Specifically, the hierarchical regressor for bi-fidelity modeling is composed of four modules: (1) the low-fidelity (LF) module explores the LF characteristics of the input; (2) the data concatenation (DC) module concatenates the output of the LF module with the input to form a vector; (3) the dimension reduction (DR) module reduces the dimension of the vector; and (4) the high-fidelity (HF) module provides the HF response of the input. The recursive method extends the resulting bi-fidelity model to the multi-fidelity case in an iterative way, where the HF information propagates to the samples at the relatively lower-fidelity levels to update their responses and the bi-fidelity models are then built based on the updated sample sets. The experimental results validate the proposed framework and show that the multi-fidelity models developed under the regression framework not only outperform the state-of-the-art models but also have a high robustness for varying sizes of HF and LF training samples, especially for very few HF samples. In addition, the algorithms (e.g., regression and DR) used in the framework can be freely changed to those appropriate to the application requirements, and thus, the proposed framework has a good applicability in practice.