Numerical Coarsening with Neural Shape Functions

No Thumbnail Available
Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
© 2023 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.
Abstract
We propose to use nonlinear shape functions represented as neural networks in numerical coarsening to achieve generalization capability as well as good accuracy. To overcome the challenge of generalization to different simulation scenarios, especially nonlinear materials under large deformations, our key idea is to replace the linear mapping between coarse and fine meshes adopted in previous works with a nonlinear one represented by neural networks. However, directly applying an end‐to‐end neural representation leads to poor performance due to over‐huge parameter space as well as failing to capture some intrinsic geometry properties of shape functions. Our solution is to embed geometry constraints as the prior knowledge in learning, which greatly improves training efficiency and inference robustness. With the trained neural shape functions, we can easily adopt numerical coarsening in the simulation of various hyperelastic models without any other preprocessing step required. The experiment results demonstrate the efficiency and generalization capability of our method over previous works.
Description

        
@article{
10.1111:cgf.14736
, journal = {Computer Graphics Forum}, title = {{
Numerical Coarsening with Neural Shape Functions
}}, author = {
Ni, Ning
and
Xu, Qingyu
and
Li, Zhehao
and
Fu, Xiao‐Ming
and
Liu, Ligang
}, year = {
2023
}, publisher = {
© 2023 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.14736
} }
Citation
Collections