用物理引导的采样和多保真度网络，大幅减少高精度流场数据需求。
Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling
- 用融合网络替代传统点积，降低预测误差50.4%。
- 通过冻结低精度网络只训练融合层，准确率比单保真度提升43.7%。
- 根据时间动态选择关键点，高精度数据量减少40%仍保持高精度。
本研究提出一种增强型多保真度深度算子网络（DeepONet）框架，用于在高保真度数据稀缺时高效预测非定常流场。核心创新包括：采用融合网络替代传统点积操作，使预测误差降低50.4%，准确率提升7.57%，训练时间减少96%；基于迁移学习的多保真度方法，冻结预训练的低保真度网络，仅训练融合网络，相比其他方法性能提升最高达76%，准确率比单保真度训练高出43.7%；以及基于物理规律的自适应采样策略，依据时间动态选择高保真度训练点，使高保真度样本需求减少40%的同时维持相近预测精度。在多个分辨率与数据集上的综合实验表明，该框架能显著降低对高保真度数据的依赖，同时保持优异预测性能，优于传统基准方法。
原文摘要 · Abstract (English)
This study presents an enhanced multi-fidelity Deep Operator Network (DeepONet) framework for efficient spatio-temporal flow field prediction when high-fidelity data is scarce. Key innovations include: a merge network replacing traditional dot-product operations, achieving 50.4% reduction in prediction error and 7.57% accuracy improvement while reducing training time by 96%; a transfer learning multi-fidelity approach that freezes pre-trained low-fidelity networks while making only the merge network trainable, outperforming alternatives by up to 76% and achieving 43.7% better accuracy than single-fidelity training; and a physics-guided subsampling method that strategically selects high-fidelity training points based on temporal dynamics, reducing high-fidelity sample requirements by 40% while maintaining comparable accuracy. Comprehensive experiments across multiple resolutions and datasets demonstrate the framework's ability to significantly reduce required high-fidelity dataset size while maintaining predictive accuracy, with consistent superior performance against conventional benchmarks.
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