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

arXiv: https://arxiv.org/abs/2412.00579 · HTML: https://mlsanity.com/paper/2412.00579/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 30 Nov 2024.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)

## Built on by (most cited first, 1 of 1)

- [Geometric Neural Operators via Lie Group-Constrained Latent Dynamics](https://mlsanity.com/paper/2602.16209/) (2026)

## Abstract (arXiv)

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.