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

arXiv: https://arxiv.org/abs/2606.16624 · HTML: https://mlsanity.com/paper/2606.16624/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 32 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 19 of 19)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [Domain Agnostic Fourier Neural Operators](https://mlsanity.com/paper/2305.00478/) (2023)
- [A Physics-Guided Neural Network Framework for Elastic Plates: Comparison of Governing Equations-Based and Energy-Based Approaches](https://mlsanity.com/paper/2010.06050/) (2020)
- [Physics-Informed Geometry-Aware Neural Operator](https://mlsanity.com/paper/2408.01600/) (2024)
- [Finite Element Operator Network for Solving Elliptic-type parametric PDEs](https://mlsanity.com/paper/2308.04690/) (2023)
- [Physics-Informed Neural Networks for Shell Structures](https://mlsanity.com/paper/2207.14291/) (2022)
- [NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers](https://mlsanity.com/paper/2511.02481/) (2025)
- [A Pretraining-Finetuning Computational Framework for Material Homogenization](https://mlsanity.com/paper/2404.07943/) (2024)
- [Sobolev Training for Operator Learning](https://mlsanity.com/paper/2402.09084/) (2024)

## Abstract (arXiv)

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.