标题： 算子学习正则化在双尺度流动问题中的宏观渗透率预测 显示英文标题

标题： Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem

摘要： 液态复合材料模塑是一种重要的纤维增强复合材料制造技术，因其成本效益高而备受关注。然而，由于对纺织品织物关键特性（如渗透率）缺乏理解，该工艺的优化面临挑战。 计算渗透系数的问题可以建模为著名的Stokes-Brinkman方程，该方程引入了一个异质参数$\beta$来区分大孔区域和纤维束区域。 在目前的工作中，我们训练了一个傅里叶神经算子来学习从异质系数$\beta$到速度场$u$的非线性映射，并恢复相应的宏观渗透率$K$。这是一个具有挑战性的反问题，因为输入和输出场的量级相差几个数量级，因此我们为损失函数引入了不同的正则化技术，并对它们进行了定量比较。 显示英文摘要

摘要： Liquid composites moulding is an important manufacturing technology for fibre reinforced composites, due to its cost-effectiveness. Challenges lie in the optimisation of the process due to the lack of understanding of key characteristic of textile fabrics - permeability. The problem of computing the permeability coefficient can be modelled as the well-known Stokes-Brinkman equation, which introduces a heterogeneous parameter $\beta$ distinguishing macropore regions and fibre-bundle regions. In the present work, we train a Fourier neural operator to learn the nonlinear map from the heterogeneous coefficient $\beta$ to the velocity field $u$, and recover the corresponding macroscopic permeability $K$. This is a challenging inverse problem since both the input and output fields span several order of magnitudes, we introduce different regularization techniques for the loss function and perform a quantitative comparison between them.