Parametric VPINN Framework for Rapid Design Exploration of Thin Slabs

Abstract: This paper proposes a robust Variational Physics-Informed Neural Network (VPINN) framework specifically tailored for the structural analysis of thin Kirchhoff-Love plates. We utilize Approximate Distance Functions (ADFs) for hard boundary constraints and a hybrid spectral variational formulation to overcome challenges associated with fourth-order partial differential equations, such as vanishing gradients and the need for C1-continuous meshing. Our VPINN framework can learn a parametric design space and enable real-time, mesh-free structural analysis, eliminating the ‘‘modeling-meshing-solving’’ cycle. The results confirm that our VPINN accurately captures critical stiffness trends and global deformation modes, satisfying the precision requirements for conceptual design and topology optimization.