AI 中文总结
本研究提出一种物理约束机器学习亚网格尺度建模方法，通过物理嵌入训练框架优化模型，可提升湍流预混火焰模拟精度，性能优于无模型、动态闭合等方案。
AI 中文摘要
采用物理嵌入的训练框架来闭合湍流预混火焰的亚网格尺度动力学。训练得到的模型对已求解的流动方程进行增强，且其训练目标为使预测的流场与可信数据匹配。对耦合的已求解方程与嵌入模型进行端到端优化，得到的模型对湍流中自由传播的预混火焰具有鲁棒性和有效性，该火焰通过单物种、单步不可逆化学反应建模。训练公式中内置了重要的守恒性、标量有界性和等变性约束。模型基于已求解流动方程的残差进行缩放，以在需要闭合的区域发挥作用。在长时间模拟中，该模型的表现优于所考虑的其他情况——无模型、动态闭合以及直接拟合残差数据的相同机器学习模型，它能校正湍流耗散和火焰运动学。最后，研究表明，与精确残差数据相比，基于预测的训练能更好地为模型提供信息。
英文摘要
A physics-embedded training framework is used to close the sub-grid-scale dynamics of turbulent premixed flames. The trained model augments the resolved flow equations and is trained to match its predicted flow field to trusted data. An end-to-end optimization of the coupled resolved equations and embedded model leads to a model that is robust and effective for a freely propagating premixed flame in turbulence, modeled by a single-species, single-step, and irreversible chemical reaction. Important constraints are built into the training formulation for conservation, scalar boundedness, and equivariance. The model is scaled based on the residual of the resolved flow equations to focus its influence where the closure is needed. It outperforms other cases considered --- no-model, dynamic closure, and the same machine learning model trained directly to fit the residual data --- for a long-time simulation, correcting the turbulence dissipation and flame kinematics. Finally, it is shown how the prediction-based training better informs the model than the precise residual data.
