Physics-informed neural network (PINN) exists some challenges, such as independent and uncorrelated drawbacks leading to convergence impediments, limited interpretability and lack of generalization. In this paper, a novel energy-informed graph transformer model is proposed to overcome the drawbacks of PINN. In the proposed model, the graph neural network-based-attention mechanism is proposed to dynamically calculate weight coefficients between objects of graph-structured data, and then to aggregate weighted combinations of the neighbor objects features to update features of the target objects. The loss function is constructed with homoscedastic uncertainty by introducing trainable scalar parameters, which can be optimized to achieve the best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. Numerical results show that the proposed method can effectively increase the efficiency, robustness and accuracy of the network approximation of forward and inverse problems of solid mechanics. Furthermore, the proposed model demonstrates excellent generalization capabilities when applied to new problem using transfer learning strategy.

中文翻译：

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用于固体力学分析的能量信息图形变压器模型


物理信息神经网络（PINN）存在一些挑战，例如独立和不相关的缺点导致收敛障碍、可解释性有限和缺乏泛化性。本文提出了一种新颖的能量信息图转换器模型来克服 PINN 的缺点。在该模型中，提出了基于图神经网络的注意力机制来动态计算图结构数据的对象之间的权重系数，然后聚合邻近对象特征的加权组合以更新目标对象的特征。通过引入可训练的标量参数来构造具有同方差不确定性的损失函数，当网络动态改变优化过程中涉及的损失函数的拓扑时，可以对其进行优化以实现网络的最佳性能。数值结果表明，该方法能够有效提高固体力学正反问题网络逼近的效率、鲁棒性和精度。此外，所提出的模型在使用迁移学习策略应用于新问题时表现出出色的泛化能力。