用神经算子预测双尺度流中材料的宏观渗透率，提升复合材料制造仿真精度。
Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem
- 用傅里叶神经算子学习非均质参数β到速度场的映射关系。
- 在多量级输入输出条件下，通过正则化提升逆问题求解精度。
- 适用于复合材料制造中的渗透率预测，尤其适合复杂织物结构建模。
液态复合材料成型是一种成本效益高的纤维增强复合材料制造技术，其工艺优化受限于对纺织材料关键特性——渗透率的理解不足。渗透系数计算可建模为经典的斯托克斯-布林克曼方程，其中引入非均质参数β以区分宏孔区与纤维束区。本文训练傅里叶神经算子，学习从非均质参数β到速度场u的非线性映射，并恢复对应的宏观渗透率K。该逆问题极具挑战性，因输入与输出场跨越多个数量级，因此我们设计多种损失函数正则化策略，并进行定量比较。
原文摘要 · Abstract (English)
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 $β$ 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 $β$ 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.
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