The Research Of Regression Model Based On Multi-fidelity Data

Besides model,the amount of training samples and the accuracy of data influence the accuracy(also called fidelity)of predictions a lot in machine learning.In many practical problems,such as computer simulations,some accurate data has expensive computational cost,which is called high fidelity(HF)data;while the data that has cheap computational cost and is obtained easily is called low fidelity(LF)data.The regression model built based on these multi-fidelity data is called multi-fidelity model.Multi-fidelity modelling aims at combining a mass of LF samples and few HF samples to construct a model that makes HF predictions for unknown inputs.As far,the proposed multi-fidelity models almost assume that the relation between HF and LF systems,or the distribution of data,or the structure of data is specific,which makes these models cannot be applied to practical problems widely.In this paper,we proposed a hierarchical regression model for multi-fidelity modelling,which is made up of four modules:1)the LF module explores the LF features of the input;2)the data concatenation(DC)module concatenates the output of LF module with the input to form a vector;3)the dimension reduction(DR)module reduces the dimension of the vector;4)the HF module provides the accurate response of the input.The experimental results validate that the multi-fidelity model built based on the hierarchical regression model not only preforms better than the state-of-the-art models,but also has good robustness which means that the model is rarely influenced by the amount of HF and LF samples.This hierarchical regression model meets the assumption of the relation of HF and LF systems,and the algorithms used in the model can be freely changed to those appropriate to the application requirements,and thus,the proposed model has good applicability in practice.In addition,we apply the data augmentation methods in machine learning to multifidelity models,hope that these methods could solve the problem that the accuracy of model is restricted to the amount of HF samples.The numerical experimental results show that some data augmentation methods could increase the accuracy of some multi-fidelity models.