MR-GVNO: A Geometry-Aware Variational Physics-Informed Neural Operator for Mindlin-Reissner Plates on Irregular Domains

2026-06-15

AI Summary

This work addresses the high computational cost of traditional finite element methods for analyzing Mindlin–Reissner plates under complex geometries, heterogeneous materials, and varying loads by proposing a geometry-aware variational physics-informed neural operator, termed MR-GVNO. The method represents irregular domains via boundary point clouds and employs separate encoders to process material fields, loading conditions, and parameters, integrating them through a cross-attention mechanism to predict deflection and rotation at arbitrary locations. MR-GVNO requires no ground-truth solution data for training, supports independent discretization of physical fields, and generalizes across diverse geometries. Numerical experiments demonstrate its high-fidelity response prediction on plates with single or double cutouts as well as L-shaped domains, achieving millisecond-scale full-field inference for both homogeneous and heterogeneous materials under deterministic or stochastic loading conditions.

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.

Problem

• Mindlin-Reissner plates
• irregular domains
• rapid response prediction
• physics-informed learning
• computational efficiency

Innovation

• geometry-aware
• variational physics-informed neural operator
• point cloud representation
• cross-attention mechanism
• mesh-free learning