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.

翻译：板壳结构在工程中应用广泛，因此亟需实现不同几何、材料和载荷下的快速响应预测。然而，传统有限元方法需要重复建模与求解，导致计算成本高昂。本研究提出一种面向Mindlin-Reissner板问题的几何感知变分神经算子，称为MR-GVNO。该方法采用边界点云表示不规则几何形状，并利用独立编码器处理空间变化材料场、压力载荷和标量物理参数。通过交叉注意力机制将这些输入与查询点信息整合，以预测任意位置的横向挠度和转角。MR-GVNO基于离散总势能导出的变分物理信息损失函数进行训练，无需标注解数据。该方法可直接处理不规则点云，且允许不同物理场独立离散化，避免插值到统一网格。对单孔、双孔及L形板的数值实验表明，该模型在同质与异质材料、均匀与随机载荷下均能实现准确响应预测。此外，模型可实现毫秒级全场推理，并展现出良好的跨几何泛化能力。