标题： 不确定性量化与神经算子的稳定性用于三维湍流预测 显示英文标题

标题： Uncertainty quantification and stability of neural operators for prediction of three-dimensional turbulence

摘要： 湍流因其混沌、多尺度的性质以及高昂的计算成本，给数值模拟带来了挑战。 传统的湍流建模方法通常在精度和长期稳定性方面存在问题。 最近的科学机器学习（SciML）模型，例如傅里叶神经算子（FNO），在求解偏微分方程（PDE）方面展现出潜力，但通常局限于一步预测，并且在长时间范围内往往表现不佳，尤其是在三维湍流情况下。 本研究提出了一种框架来评估神经算子模型在湍流流动中的可靠性。 以三维强迫同质各向同性湍流（HIT）作为基准，我们从不确定性量化（UQ）、误差传播以及初始扰动敏感性等方面评估了这些模型。 使用误差分布分析和自相关函数（ACF）等统计工具来评估预测的鲁棒性和时间一致性。 我们提出的模型——因子隐式FNO（F-IFNO），通过在预测过程中引入隐式分解，提高了长期稳定性和准确性。 它在平衡准确度、稳定性与效率方面优于常规的大涡模拟（LES）和其他基于FNO的模型。 结果强调了在开发用于湍流系统的鲁棒神经算子框架时，预测约束、时间间隔选择以及不确定性量化的重要性。 显示英文摘要

摘要： Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine learning (SciML) models, such as Fourier Neural Operators (FNO), show promise in solving PDEs, but are typically limited to one-step-ahead predictions and often fail over long time horizons, especially in 3D turbulence. This study proposes a framework to assess the reliability of neural operator models in turbulent flows. Using three-dimensional forced homogeneous isotropic turbulence (HIT) as a benchmark, we evaluate models in terms of uncertainty quantification (UQ), error propagation, and sensitivity to initial perturbations. Statistical tools such as error distribution analysis and autocorrelation functions (ACF) are used to assess predictive robustness and temporal coherence. Our proposed model, the factorized-implicit FNO (F-IFNO), improves long-term stability and accuracy by incorporating implicit factorization into the prediction process. It outperforms conventional LES and other FNO-based models in balancing accuracy, stability, and efficiency. The results highlight the importance of prediction constraints, time interval selection, and UQ in developing robust neural operator frameworks for turbulent systems.