基于稀疏神经核的多保真度代理模型

李欣然; 连峰; 贾家兴

doi:10.7638/kqdlxxb-2024.0180

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基于稀疏神经核的多保真度代理模型

研究论文 | 更新时间：2026-05-28

- 基于稀疏神经核的多保真度代理模型
- A multi-fidelity surrogate model with sparse neural kernel
- 空气动力学学报 2026年44卷第2期页码：37-49
- 作者机构：
  
  西安交通大学电子与信息学部自动化科学与工程学院,西安,710049
- 作者简介：
  
  李欣然（2000—），女，山东济南人，硕士研究生，研究方向：气动数据建模与融合. E-mail：lxr913@stu.xjtu.edu.cn
  连峰*，教授，研究方向：智能流体力学，多目标跟踪. E-mail：lianfeng1981@mail.xjtu.edu.cn
- 基金信息：
  
  国家自然科学基金（62173266）
- DOI：10.7638/kqdlxxb-2024.0180
  中图分类号： TP391;V211.3
- 纸质出版：2026
- 稿件说明：
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李欣然, 连峰, 贾家兴. 基于稀疏神经核的多保真度代理模型[J]. 空气动力学学报, 2026, 44(2): 37−49.

Li Xinran, Lian Feng, Jia Jiaxing. A multi-fidelity surrogate model with sparse neural kernel[J]. 2026, 44(2): 37-49.
李欣然, 连峰, 贾家兴. 基于稀疏神经核的多保真度代理模型[J]. 空气动力学学报, 2026, 44(2): 37−49. DOI： 10.7638/kqdlxxb-2024.0180

Li Xinran, Lian Feng, Jia Jiaxing. A multi-fidelity surrogate model with sparse neural kernel[J]. 2026, 44(2): 37-49. DOI： 10.7638/kqdlxxb-2024.0180.

摘要

在航空航天技术领域，代理模型发挥着关键作用。为平衡代理模型的训练成本与预测精度，需要发展能够有效挖掘多保真度数据间潜在相关性的建模方法。针对现有模型依赖预设核函数、缺乏数据自适应性的问题，提出了一种基于稀疏混合专家神经核（mixture of experts neural kernel

MoENK）的多保真度代理模型。MoENK通过线性混合和乘积混合基本单元构造新核函数，选择性屏蔽中间结果以过滤噪声，并应用于多任务高斯过程中。将该方法应用于3个函数示例和2个翼型算例中，结果表明该方法的预测精度有较大提升，尤其在NACA0012翼型阻力系数的预测中，相较于次佳方法LR-MFS，RMSE和MAE分别降低了40.42%和44.70%。证实了所提出的MoENK核函数能够不依赖预设核函数进行自适应预测，具有良好的泛化能力和鲁棒性，为工程系统的代理模型构建提供了新的工具。

Abstract

Surrogate models play a crucial role in aerospace technology. To offer a trade-off between training costs and model accuracy

we introduce multi-fidelity surrogate models based on Gaussian processes. These models leverage data with varying levels of fidelity

to enhance predictive performance while simultaneously minimizing computational expenses. By integrating information from both high-fidelity and low-fidelity datasets

multi-fidelity models can achieve higher accuracy without the need for extensive high-fidelity data

which is often costly and time-consuming to obtain. However

existing multi-fidelity GP models predominantly rely on empirically predetermined kernel functions. These kernel functions are typically selected based on prior experience and general assumptions about the data

without considering the specific characteristics and underlying structures of the datasets at hand. As a result

these kernels are not tailored to the data. To overcome these challenges

this paper introduced a novel approach to constructing kernel functions that are specifically designed to uncover and exploit the latent correlations between datasets of different fidelities. To address these issues

we first proposd the mixture of experts neural kernel (MoENK) which construct a more powerful kernel based on some basic kernels. In MoENK

we used two primary components: MoE-Linear and MoE-Product to selectively mask intermediate results

thereby effectively filtering out noise which may introduce negative transfer. This was then applied to multi-task Gaussian processes

which allows for the sharing of information across different fidelity levels

thereby improving the robustness and accuracy of the surrogate models. To rigorously evaluate the performance of the proposed method

we conducted a series of experiments using three benchmark function examples and two airfoil cases. It exhibited particularly notable advantages in predicting the high-dimensional drag coefficient scenario of the NACA0012 airfoil

reducing RMSE and MAE by 40.42% and 44.70%

respectively

compared to the suboptimal method

LR-MFS. These results confirm that the proposed MoENK kernel function can adaptively predict without relying on predefined kernels

offering strong generalization capabilities and robustness. This provides a new tool for constructing surrogate models in engineering systems.

关键词

Keywords

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