Preconditioned Variational Physics-informed Neural Operator (P-VINO) for membranes and Mindlin plates

In this work, the Preconditioned Variational Physics-informed Neural Operator (P-VINO) is proposed. This framework exploits the potential of Physics-informed Neural Operators, which are capable of learning the mapping from parameter-dependent inputs to the solution. In addition, the Physics-informed mechanism eliminates the need for a large training dataset. The framework is applied to linear membrane and Mindlin plate problems and relies on a variational formulation. Among the distinctive features of P-VINO, two are particularly relevant for overcoming key limitations in the data-free training of the Fourier Neural Operator. Firstly, a preconditioning technique is implemented to tackle ill-conditioned issues. Secondly, a FEM-based conforming strategy is implemented to preserve the FEM flexibility in defining loading and boundary conditions along any edge of the structure. The results are presented for both membranes and Mindlin plates, demonstrating that P-VINO improves convergence, energetic consistency with finite element solutions, and accurately captures the structural response even for ill-conditioned problems, suggesting its potential for fast parametric structural analyses.