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.

翻译：液态复合材料成型因其成本效益而成为纤维增强复合材料的重要制造技术。由于对纺织织物关键特性——渗透率——的理解不足，该工艺的优化面临挑战。渗透率系数的计算问题可建模为著名的Stokes-Brinkman方程，该方程引入异质参数$\beta$以区分大孔区域与纤维束区域。在本研究中，我们训练傅里叶神经算子学习从异质系数$\beta$到速度场$u$的非线性映射，并恢复相应的宏观渗透率$K$。由于输入场与输出场均跨越多个数量级，这是一个具有挑战性的反问题，我们为此在损失函数中引入不同的正则化技术，并对它们进行了定量比较。