T. Rabczuk
Publications
MR-GVNO: A Geometry-Aware Variational Physics-Informed Neural Operator for Mindlin-Reissner Plates on Irregular Domains
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.
Dmsh: A Multi-Agent Reinforcement Learning Framework for All-Quad Mesh Generation
Generating high-quality meshes for arbitrary geometries remains a fundamental bottleneck in computational engineering, often demanding heuristic tuning and semi-manual workflows. In this paper, we introduce Dmsh, a first fully automated reinforcement learning pipeline that unifies geometric decomposition and quadrilateral mesh generation within a single learning-based framework. Dmsh decomposes the problem through three coordinated agents handling topology simplification, geometric regularization, and mesh generation. The meshing process is formulated as a Markov Decision Process and solved using a parametric Soft Actor-Critic architecture with decoupled critics, enabling efficient exploration of a hybrid discrete-continuous action space. A curriculum learning strategy ensures scalability from simple domains to highly complex geometries, suppressing seed variance. By design, the recursive decomposition enables parallel meshing of subregions, yielding globally conforming all-quadrilateral meshes without post hoc correction. Across a wide range of benchmarks, Dmsh consistently outperforms existing methods in automation, robustness, and mesh quality, establishing a new paradigm for learning-based mesh generation.