Conformal Predictions Enhanced Expert-guided Meshing with Graph Neural
  Networks
Amin Heyrani Nobari Justin Rey Suhas Kodali Matthew Jones Faez Ahmed
Computational Fluid Dynamics (CFD) is widely used in different engineering
fields, but accurate simulations are dependent upon proper meshing of the
simulation domain. While highly refined meshes may ensure precision, they come
with high computational costs. Similarly, adaptive remeshing techniques require
multiple simulations and come at a great computational cost. This means that
the meshing process is reliant upon expert knowledge and years of experience.
Automating mesh generation can save significant time and effort and lead to a
faster and more efficient design process. This paper presents a machine
learning-based scheme that utilizes Graph Neural Networks (GNN) and expert
guidance to automatically generate CFD meshes for aircraft models. In this
work, we introduce a new 3D segmentation algorithm that outperforms two
state-of-the-art models, PointNet++ and PointMLP, for surface classification.
We also present a novel approach to project predictions from 3D mesh
segmentation models to CAD surfaces using the conformal predictions method,
which provides marginal statistical guarantees and robust uncertainty
quantification and handling. We demonstrate that the addition of conformal
predictions effectively enables the model to avoid under-refinement, hence
failure, in CFD meshing even for weak and less accurate models. Finally, we
demonstrate the efficacy of our approach through a real-world case study that
demonstrates that our automatically generated mesh is comparable in quality to
expert-generated meshes and enables the solver to converge and produce accurate
results. Furthermore, we compare our approach to the alternative of adaptive
remeshing in the same case study and find that our method is 5 times faster in
the overall process of simulation. The code and data for this project are made
publicly available at https://github.com/ahnobari/AutoSurf.