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With the rapid development of deep learning neural networks, new solutions have emerged for addressing fluid flow problems in porous media. Combining data-driven approaches with physical constraints has become a hot research direction, with physics-informed neural networks (PINNs) being the most popular hybrid model. PINNs have gained widespread attention in subsurface fluid flow simulations due to their low computational resource requirements, fast training speeds, strong generalization capabilities, and broad applicability. Despite success in homogeneous settings, standard PINNs face challenges in accurately calculating flux between irregular Eulerian cells with disparate properties and capturing global field influences on local cells. This limits their suitability for heterogeneous reservoirs and the irregular Eulerian grids frequently used in reservoir. To address these challenges, this study proposes a physics-informed graph neural network (PIGNN) model. The PIGNN model treats the entire field as a whole, integrating information from neighboring grids and physical laws into the solution for the target grid, thereby improving the accuracy of solving partial differential equations in heterogeneous and Eulerian irregular grids. The optimized model was applied to pressure field prediction in a spatially heterogeneous reservoir, achieving an average L2 error and R2 score of 6.710 × 10−4 and 0.998, respectively, which confirms the effectiveness of model. Compared to the conventional PINN model, the average L2 error was reduced by 76.93%, the average R2 score increased by 3.56%. Moreover, evaluating robustness, training the PIGNN model using only 54% and 76% of the original data yielded average relative L2 error reductions of 58.63% and 56.22%, respectively, compared to the PINN model. These results confirm the superior performance of this approach compared to PINN.

Shape prediction of deformable linear objects (DLO) plays critical roles in robotics, medical devices, aerospace, and manufacturing, especially in manipulating objects such as cables, wires, and fibers. Due to the inherent flexibility of DLO and their complex deformation behaviors, such as bending and torsion, it is challenging to predict their dynamic characteristics accurately. Although the traditional physical modeling method can simulate the complex deformation behavior of DLO, the calculation cost is high and it is difficult to meet the demand of real-time prediction. In addition, the scarcity of data resources also limits the prediction accuracy of existing models. To solve these problems, a method of fiber shape prediction based on a physical information graph neural network (PIGNN) is proposed in this paper. This method cleverly combines the powerful expressive power of graph neural networks with the strict constraints of physical laws. Specifically, we learn the initial deformation model of the fiber through graph neural networks (GNN) to provide a good initial estimate for the model, which helps alleviate the problem of data resource scarcity. During the training process, we incorporate the physical prior knowledge of the dynamic deformation of the fiber optics into the loss function as a constraint, which is then fed back to the network model. This ensures that the shape of the fiber optics gradually approaches the true target shape, effectively solving the complex nonlinear behavior prediction problem of deformable linear objects. Experimental results demonstrate that, compared to traditional methods, the proposed method significantly reduces execution time and prediction error when handling the complex deformations of deformable fibers. This showcases its potential application value and superiority in fiber manipulation.