面向变精度仿真数据建模分析的多任务学习方法比较研究

A Comparative Study on Multi-task Learning Methods for Modeling and Analysis of Multi-fidelitySimulation Data

多任务学习(Multi-task Learning,MTL)是利用多个目标任务之间的关联性,实现跨任务知识迁移和共享,从而提高预测精度的一种数据驱动的机器学习范式。基于数值仿真器工程设计问题中经常存在多精度建模分析场景,即采用不同精度的数值仿真器获取数据进行建模。在上述场景中,仿真器的高/低计算精度可以被视为两种目标任务,同时,由于高/低精度数据针对的是同一个研究对象,彼此具有很强的相关性。其中的关键是如何从便宜、丰富的低精度数据中迁移出共享知识以提高基于昂贵、稀少的高精度数据的学习模型的预测质量。本文重点研究基于高斯过程(Gaussian Process,GP)或Kriging模型的多任务统计学习方法及其在高/低精度仿真建模分析方面的应用。首先,本文在典型多精度数值算例上对比分析了单任务Kriging模型,以及三种多任务(精度)模型CoKriging、MTGP(Multi-task Gaussian Process)和SDK(Simple Discrepancy Framework by Kriging,SDK)的特点及预测能力。最后,本文基于多精度仿真数据使用Kriging模型、MTGP模型和CoKriging模型预测RAE2822翼型的空气动力系数。结果表明:将多任务学习应用于多精度工程建模分析可以提高预测的准确度,进而提高产品的设计效率。

Multi-task learning(MTL)is a machine learning paradigm that utilizes the correlation between multiple tasks to realize knowledge transfer and sharing across tasks so as to improve the prediction accuracy.This paper aims at the scenario of multi-fidelity modeling analysis,that is,the studied problem could be simulated with different fidelities,which can be regarded as different tasks.Since the high and low fidelity data is targeted at the same problem,they are strongly correlated.Hence,the key is how to transfer shared knowledge from the cheap and abundant low-fidelity data in order to improve the prediction quality of model built upon the expensive and scarce high-fidelity data.This paper focuses on the study of Gaussian process(GP)(also known as Kriging)based multi-task statistical models,and their application on the modeling of high-and low-fidelity data.Firstly,this paper compares and analyzes the characteristics and performance of the single-task Kriging,and three multi-task models including CoKriging,MTGP(multi-task Gaussian process)and SDK(simple discrepancy framework by Kriging)on numerical benchmarks.Thereafter,the Kriging model,the MTGP model and the CoKriging model trained on multi-fidelity simulation data are used to predict the aerodynamic coefficient of the RAE2822 airfoil.The results show that the application of multi-task learning to multi-fidelity engineering modeling analysis can improve the accuracy of prediction and thus improve the efficiency of product design.