GA-VINO: A Geometry-Aware Variational Physics-informed Neural Operator for Mindlin-Reissner Plates

Plate and shell structures are widely used in engineering fields. Rapid response prediction for such structures under complex geometries, heterogeneous materials, and varying loads is important for engineering design, but conventional numerical methods usually require repeated modeling and solution when the physical configuration changes. To address this issue, this study proposes a geometry-aware variational physics-informed neural operator (GA-VINO) for Mindlin-Reissner plates. GA-VINO represents the plate geometry using boundary point clouds and incorporates a material encoder, a load encoder, and a scalar-parameter branch to handle spatially random material fields, spatially varying pressure loads, and sample-level uniform parameters. Through multi-branch point cloud encoding and cross-attention, GA-VINO fuses geometric, material, loading, and query point information, and predicts the transverse deflection and rotations at arbitrary query locations. Unlike conventional data-driven neural operators, GA-VINO requires no labeled solution data during training. Instead, it minimizes a variational physics-informed loss constructed from the discretized total potential energy of the Mindlin-Reissner plate. Compared with grid-based neural operators, GA-VINO directly processes irregular point clouds and allows different physical fields to be discretized on different point sets, avoiding forced interpolation onto a common grid. The method is validated on multiple examples involving different geometries, material fields, and load distributions. The results show that GA-VINO achieves promising accuracy in deflection, rotation, gradient-sensitive, and energy-based metrics, completes full-field inference for new samples within milliseconds, and exhibits promising cross-geometry generalization capability.