Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem
This work addresses permeability prediction for optimizing liquid composites molding in fiber reinforced composites manufacturing, representing an incremental improvement with domain-specific regularization methods.
The paper tackles the problem of predicting macroscopic permeability in dual-scale flow problems for liquid composites molding by training a Fourier neural operator to learn the nonlinear map from a heterogeneous coefficient to velocity fields, and introduces regularization techniques for the loss function to address challenges in this inverse problem.
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.