In this work, we provide a mathematical formulation for error propagation in flow trajectory prediction using data-driven turbulence closure modeling. Under the assumption that the predicted state of a large eddy simulation prediction must be close to that of a subsampled direct numerical simulation, we retrieve an upper bound for the prediction error when utilizing a data-driven closure model. We also demonstrate that this error is significantly affected by the time step size and the Jacobian which play a role in amplifying the initial one-step error made by using the closure. Our analysis also shows that the error propagates exponentially with rollout time and the upper bound of the system Jacobian which is itself influenced by the Jacobian of the closure formulation. These findings could enable the development of new regularization techniques for ML models based on the identified error-bound terms, improving their robustness and reducing error propagation.

通过数据驱动的涡流闭包建模，我们对流动轨迹预测中的误差传播提供了数学化的表述，分析了误差传播的影响因素，并且指出这些发现可以为基于机器学习模型的新的正则化技术提供改进的方向。

关于大涡模拟的数据驱动闭合模型误差分析的说明