English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this work, we have applied physics-informed neural networks (PINN) forsolving mesh deformation problems. We used the collocation PINN method tocapture the new positions of the vertex nodes while preserving the connectivityinformation. We use linear elasticity equations for mesh deformation. Toprevent vertex collisions or edge overlap, the mesh movement in this work isconducted in steps with relatively small movements. For moving boundaryproblems, the exact position of the boundary is essential for having anaccurate solution. However, PINNs are frequently unable to satisfy Dirichletboundary conditions exactly. To overcome this issue, we have used hard boundarycondition enforcement to automatically satisfy Dirichlet boundary conditions.Specifically, we first trained a PINN with soft boundary conditions to obtain aparticular solution. Then, this solution was tuned with exact boundarypositions and a proper distance function by using a new PINN considering onlythe equation residual. To assess the accuracy of our approach, we used theclassical translation and rotation tests and compared them with a proper meshquality metric considering the change in the element area and shape. Theresults show the accuracy of this approach is comparable with that of finiteelement solutions. We also solved different moving boundary problems,resembling commonly used fluid-structure interaction problems. This workprovides insight into using PINN for mesh-deformation problems without needinga discretization scheme with reasonable accuracy.

Physics-Informed Neural Networks for Mesh Deformation with Exact Boundary Enforcement