用少量高精度数据，融合大量低精度数据，精准预测气动性能并给出可信误差范围。
Multi-fidelity aerodynamic data fusion by autoencoder transfer learning
- 用自编码器迁移学习，从海量低精度数据中提取物理特征作为知识库。
- 仅需极少高精度样本，即可实现对2D/3D机翼压力分布的高精度预测。
- 首次在极小数据下实现95%以上置信度的可解释不确定性量化，适合工程仿真场景。
高精度气动模拟虽准确但计算成本极高，限制了其在数据驱动建模中的应用。为此，本文提出一种多保真度深度学习框架，结合基于自编码器的迁移学习与新提出的多分裂共形预测（MSCP）策略，在极端数据稀缺条件下实现带不确定性的气动数据融合。该方法利用大量低保真（LF）数据学习紧凑的隐空间物理表征，作为冻结的知识库，供解码器使用少量高保真（HF）样本进行微调。在二维NACA机翼和三维跨音速机翼的压力分布数据集上测试表明，模型有效修正了低保真偏差，仅用极少HF训练数据即实现高精度压力预测。此外，MSCP框架生成的置信区间具有强鲁棒性，点对点覆盖率超过95%。该方法兼具极强的数据效率与不确定性量化能力，为数据稀缺环境下的气动回归提供了可扩展且可靠的新方案。
原文摘要 · Abstract (English)
Accurate aerodynamic prediction often relies on high-fidelity simulations; however, their prohibitive computational costs severely limit their applicability in data-driven modeling. This limitation motivates the development of multi-fidelity strategies that leverage inexpensive low-fidelity information without compromising accuracy. Addressing this challenge, this work presents a multi-fidelity deep learning framework that combines autoencoder-based transfer learning with a newly developed Multi-Split Conformal Prediction (MSCP) strategy to achieve uncertainty-aware aerodynamic data fusion under extreme data scarcity. The methodology leverages abundant Low-Fidelity (LF) data to learn a compact latent physics representation, which acts as a frozen knowledge base for a decoder that is subsequently fine-tuned using scarce HF samples. Tested on surface-pressure distributions for NACA airfoils (2D) and a transonic wing (3D) databases, the model successfully corrects LF deviations and achieves high-accuracy pressure predictions using minimal HF training data. Furthermore, the MSCP framework produces robust, actionable uncertainty bands with pointwise coverage exceeding 95%. By combining extreme data efficiency with uncertainty quantification, this work offers a scalable and reliable solution for aerodynamic regression in data-scarce environments.
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