Distinguishing genuine news from false information is crucial in today’s digital era. Most of the existing methods are based on either the traditional neural network sequence model or graph neural network model that has become more popularity in recent years. Among these two types of models, the latter solve the former’s problem of neglecting the correlation among news sentences. However, one layer of the graph neural network only considers the information of nodes directly connected to the current nodes and omits the important information carried by distant nodes. As such, this study proposes the Extendable-to-Global Heterogeneous Graph Attention network (namely EGHGAT) to manage heterogeneous graphs by cleverly extending local attention to global attention and addressing the drawback of local attention that can only collect information from directly connected nodes. The shortest distance matrix is computed among all nodes on the graph. Specifically, the shortest distance information is used to enable the current nodes to aggregate information from more distant nodes by considering the influence of different node types on the current nodes in the current network layer. This mechanism highlights the importance of directly or indirectly connected nodes and the effect of different node types on the current nodes, which can substantially enhance the performance of the model. Information from an external knowledge base is used to compare the contextual entity representation with the entity representation of the corresponding knowledge base to capture its consistency with news content. Experimental results from the benchmark dataset reveal that the proposed model significantly outperforms the state-of-the-art approach. Our code is publicly available at https://github.com/gyhhk/EGHGAT_FakeNewsDetection.

This paper proposes the multi-scale neural networks method based on Runge-Kutta to solve unsteady partial differential equations. The method uses q-order Runge-Kutta to construct the time iteratione scheme, and further establishes the total loss function of multiple time steps, which is to realize the parameter sharing of neural networks with multiple time steps, and to predict the function value at any moment in the time domain. Besides, the m-scaling factor is adopted to speed up the convergence of the loss function and improve the accuracy of the numerical solution. Finally, several numerical experiments are presented to demonstrate the effectiveness of the proposed method.

The velocity-correction projection method for the 2D/3D time-dependent micropolar fluid equations is considered. In this method, the first-order and second-order backward difference schemes are applied for time discretization and conforming finite element is adopted for spatial discretization. The unconditional stability of the first-order and second-order time semi-discrete velocity-correction projection methods are given, and the error estimation of the first-order semi-discrete scheme is analyzed. The stability analysis of the first-order fully discrete scheme is also given. Finally, several numerical examples are presented to show the efficiency of the proposed method.

With the progress of machine learning in many fields, physics-informed neural networks provide new ideas for solving partial differential equations, but this method is difficult to obtain high-precision numerical solutions. Absorbing the philosophy of physics-informed neural network and the two-grid solution of partial differential equations, this paper puts forward the deep learning method based on two-grid for solving stationary partial differential equations. For the neural network to solve the multi-objective problem, the dynamic weight strategy is adopted to balance the numerical difference between the items in the loss function, and alleviate the gradient ill-conditioned phenomenon. Finally, this paper gives several numerical experiments to verify the effectiveness of the deep learning method combined with dynamic weight strategy in improving the calculation accuracy.

Main difficulties of numerically solving the 3D time-dependent Navier-Stokes equations are incompressibility condition, nonlinearity and longtime integration. First, we discuss the research progress and recent achievements in the highly efficient fully discrete finite element method for solving the 3D time-dependent Navier-Stokes equations. Secondly, we expound the stability and error estimates of the finite element spatial discrete solution and the optimal error estimates of the highly efficient fully discrete finite element method for solving the 3D time-dependent Navier-Stokes equations.

In this paper, the finite element approximation of the convection-diffusion-reaction equation on surfaces is studied. By introducing middle variables of different forms, the original equation is transformed into the equivalent, first-order mixed form. Using the idea of mixed finite element, this paper directly uses the mixed stabilization method of low order finite element pair(P₁-P₁) approximation. The method not only satisfies the well-posed condition, but also can effectively capture the non-physical oscillation caused by convective dominance. Finally, the numerical results show that the convergence results are consistent with the known theory.