Applying Convolutional Neural Networks to data on unstructured meshes with space-filling curves
File(s)
Published version
OA Location
Author(s)
Heaney, Claire E
Li, Yuling
Matar, Omar K
Pain, Christopher C
Type
Journal Article
Abstract
This paper presents the first classical Convolutional Neural Network (CNN) that can be applied directly to data from unstructured finite element meshes or control volume grids. CNNs have been hugely influential in the areas of image classification and image compression, both of which typically deal with data on structured grids. Unstructured meshes are frequently used to solve partial differential equations and are particularly suitable for problems that require the mesh to conform to complex geometries or for problems that require variable mesh resolution. Central to our approach are space-filling curves, which traverse the nodes or cells of a mesh tracing out a path that is as short as possible (in terms of numbers of edges) and that visits each node or cell exactly once. The space-filling curves (SFCs) are used to find an ordering of the nodes or cells that can transform multi-dimensional solutions on unstructured meshes into a one-dimensional (1D) representation, to which 1D convolutional layers can then be applied. Although developed in two dimensions, the approach is applicable to higher dimensional problems. To demonstrate the approach, the network we choose is a convolutional autoencoder (CAE), although other types of CNN could be used. The approach is tested by applying CAEs to data sets that have been reordered with a space-filling curve. Sparse layers are used at the input and output of the autoencoder, and the use of multiple SFCs is explored. We compare the accuracy of the SFC-based CAE with that of a classical CAE applied to two idealised problems on structured meshes, and then apply the approach to solutions of flow past a cylinder obtained using the finite-element method and an unstructured mesh.
Date Issued
2024-07-01
Date Acceptance
2024-03-01
Citation
Neural Networks, 2024, 175
ISSN
0893-6080
Publisher
Elsevier
Journal / Book Title
Neural Networks
Volume
175
Copyright Statement
© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
https://www.ncbi.nlm.nih.gov/pubmed/38593555
PII: S0893-6080(24)00122-9
Subjects
Autoencoder
Computer Science
Computer Science, Artificial Intelligence
ConvNets
Convolutional neural network
DECOMPOSITION
FLOWS
Life Sciences & Biomedicine
Neurosciences
Neurosciences & Neurology
OPTIMIZATION
REDUCED-ORDER MODEL
SCHEME
Science & Technology
Space-filling curve
Technology
Unstructured meshes
Publication Status
Published
Coverage Spatial
United States
Article Number
106198
Date Publish Online
2024-03-11