MR-GVNO: A Geometry-Aware Variational Physics-Informed Neural Operator for Mindlin-Reissner Plates on Irregular Domains
2026-06-15 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors created a new method called MR-GVNO to quickly predict how plate and shell structures bend and twist under different shapes, materials, and loads. Instead of using traditional, slow simulations, their approach directly works with irregular geometric data and material details without needing lots of labeled examples. They train the model using physics rules so it learns solutions by itself. Tests show the method predicts accurately and very fast, even on different shapes it hasn’t seen before.
Mindlin-Reissner plate theoryvariational neural operatorfinite element methodphysics-informed learningcross-attentionpoint cloudsstructural response predictionheterogeneous materials
Authors
Siqi Wang, Daobo Sun, Yizheng Wang, Yilong Zhang, Yabin Jin, Xiaoying Zhuang, Timon Rabczuk
Abstract
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.