Inversion of the spatially dependent mechanical field based on PIGNNs

Abstract. Deep learning (DL) is a promising approach to predicting physical phenomena, and has been widely researched in the inversion of the spatially dependent mechanical field due to their remarkable fitting abilities. The traditional physics-informed neural networks (PINNs) disregard the locality of physical evolution processes, which makes the model results lack representation ability and effectiveness. Physics-informed graph neural networks (PIGNNs) can adapt to various types of two-dimensional unstructured grids due to their flexible manipulative data, which enhances the interpretability of the model. Therefore, in this work, a physics and data-driven graph neural networks model is constructed for inversion of the spatially dependent parameter. This model combines traditional numerical methods with unstructured data, and embedded physical information into the graph networks model in the form of discrete differentiation, which made the model have better generalization and interpretability. To verify the feasibility of the model, parameter inversion is performed on plane structures with varying spatially dependent mechanical fields. The results demonstrate that PIGNNs can accurately identify the spatial stiffness variations, and its accuracy in inverting spatially dependent stiffness surpasses that of traditional PINNs. This indicates that the model has strong potential for solving inverse problems related to mechanical parameters.