用傅里叶神经算子加速二维湍流模拟，提升长期预测稳定性。
Fourier neural operators for spatiotemporal dynamics in two-dimensional turbulence
- 将FNO与PDE求解器结合，实现快速流体模拟
- 验证了训练所需时空分辨率数据量要求
- 揭示纯数据驱动方法在长期模拟中的陷阱
大多数现实应用中的高保真直接数值模拟在计算上仍面临巨大挑战。尽管已有多种机器学习方法被提出以降低计算成本，但它们在长时间预测中常出现不稳定或非物理解。本文发现，基于傅里叶神经算子（FNO）的模型结合偏微分方程（PDE）求解器，可显著加速流体动力学模拟，从而缓解大规模湍流模拟的计算负担。我们将FNO模型视为与PDE求解器同等地位的工具，探讨了构建湍流预训练模型所需的时空数据量及时间分辨率。同时，分析了纯数据驱动方法在长期湍流模拟中需规避的潜在问题，以确保机器学习模型具备成为可靠、高效工具的可行性与竞争力。
原文摘要 · Abstract (English)
High-fidelity direct numerical simulation of turbulent flows for most real-world applications remains an outstanding computational challenge. Several machine learning approaches have recently been proposed to alleviate the computational cost even though they become unstable or unphysical for long time predictions. We identify that the Fourier neural operator (FNO) based models combined with a partial differential equation (PDE) solver can accelerate fluid dynamic simulations and thus address computational expense of large-scale turbulence simulations. We treat the FNO model on the same footing as a PDE solver and answer important questions about the volume and temporal resolution of data required to build pre-trained models for turbulence. We also discuss the pitfalls of purely data-driven approaches that need to be avoided by the machine learning models to become viable and competitive tools for long time simulations of turbulence.
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