在具有显著保真度差异的复杂PDE问题上对多保真度神经算子进行基准测试
Benchmarking Multi-fidelity Neural Operators on Complex PDE Problems with Non-trivial Fidelity Differences
浏览论文内容
中文总结 AI 辅助
该研究在含显著模型差异的复杂PDE问题上基准测试多保真度神经算子，发现迁移学习可提升精度，是高效多保真PDE替代建模的可靠方法。
中文摘要 AI 辅助
求解PDE控制的物理问题计算成本高昂，限制了训练神经算子所需的高保真（HF）数据的可用性，而神经算子通常需要大量数据集。多保真度学习通过将丰富的低保真（LF）数据与有限的HF样本相结合来解决这一问题。为了评估几种多保真度神经算子策略，包括两步法、残差法、中间法和迁移学习，我们在四个PDE测试用例中进行了系统评估：两个标准基于网格的问题、一个具有LF-HF控制方程差异的修正达西流，以及一个具有时间动态的非定常烟流入。大多数现有研究聚焦于基于网格的LF-HF差异，但现实世界中的差异（如CFD中RANS与LES模型之间的差异）可能更为复杂。为了捕捉这些更具挑战性的场景，我们引入了两个新的测试用例，专门设计用于模拟超出简单网格分辨率差异的非平凡LF-HF不匹配，从而能够在显著模型差异下对多保真度策略进行更现实的评估。我们发现，在LF-HF差异较大时，直接将LF预测输入HF模型的方法容易出现误差放大，尤其是在自回归设置中。相比之下，迁移学习（使用LF训练的权重初始化HF模型）通过提供由HF数据优化的稳健先验，始终提高了准确性。这些结果凸显了将迁移学习确立为高效多保真度PDE替代建模可靠方法的重要性。
英文摘要
Solving PDE-governed physical problems is computationally expensive, limiting the availability of high-fidelity (HF) data for training neural operators, which typically require large datasets. Multi-fidelity learning addresses this by combining abundant low-fidelity (LF) data with limited HF samples. To evaluate several multi-fidelity neural operator strategies, including two-step, residual, intermediate, and transfer learning, we conduct a systematic assessment across four PDE test cases: two standard grid-based problems, a modified Darcy flow with LF-HF governing equation discrepancies, and an unsteady smoke inflow with temporal dynamics. Most prior studies focus on grid-based LF-HF differences, but real-world discrepancies, such as those between RANS and LES models in CFD, can be more complex. To capture these more challenging scenarios, we introduce two new test cases specifically designed to emulate nontrivial LF-HF mismatch beyond simple grid-resolution differences, enabling a more realistic assessment of multi-fidelity strategies under substantial model discrepancies. We find that methods directly feeding LF predictions into HF models are prone to error amplification under large LF-HF discrepancies, particularly in autoregressive settings. In contrast, transfer learning, which uses LF-trained weights to initialise the HF model, consistently improves accuracy by providing a robust prior refined with HF data. These results highlight the importance of establishing transfer learning as a reliable approach for efficient multi-fidelity PDE surrogate modelling.
