MR-GVNO: A Geometry-Aware Variational Physics-Informed Neural Operator for Mindlin-Reissner Plates on Irregular Domains
For engineers needing rapid plate response prediction, MR-GVNO reduces computational cost compared to finite element methods by enabling fast inference without labeled data.
MR-GVNO achieves millisecond-level full-field inference for Mindlin-Reissner plates on irregular domains, with accurate predictions under varying geometries, materials, and loads, and demonstrates favorable cross-geometry generalization.
Plate and shell structures are widely used in engineering, making rapid response prediction under varying geometries, materials, and loads highly desirable. However, conventional finite element methods require repeated modeling and solution, resulting in high computational costs. This study proposes a geometry-aware variational neural operator for Mindlin-Reissner plate problems, termed MR-GVNO. The method uses boundary point clouds to represent irregular geometries and employs separate encoders for spatially varying material fields, pressure loads, and scalar physical parameters. A cross-attention mechanism integrates these inputs with query point information to predict transverse deflections and rotations at arbitrary locations. MR-GVNO is trained without labeled solution data using a variational physics-informed loss derived from the discretized total potential energy. It directly processes irregular point clouds and allows different physical fields to be discretized independently, avoiding interpolation onto a common grid. Numerical experiments on single-hole, double-hole, and L-shaped plates demonstrate accurate response prediction under homogeneous and heterogeneous materials and uniform and random loads. The model also achieves millisecond-level full-field inference and favorable cross-geometry generalization.