论文标题
有限元方法增强神经网络，用于逆问题和反问题
Finite Element Method-enhanced Neural Network for Forward and Inverse Problems
论文作者
论文摘要
我们介绍了一种新型混合方法，将经典有限元方法（FEM）与神经网络相结合，以创建一个良好的前进和逆问题替代模型。有限元方法的残差和来自神经网络的自定义损失功能合并以形成算法。有限元方法增强神经网络混合模型（FEM-NN混合）是数据效率和物理符合的。在实时模拟，不确定性量化和优化的情况下，该方法可用于替代模型。在反问题的情况下，它可用于更新模型。用示例证明了该方法，结果和性能的准确性与传统的网络培训方式和经典有限元方法进行了比较。向前分解算法的应用显示了对高层建筑物的不确定性量化。在速度依赖性轴承系数的识别流体轴承中证明了逆算法。此类混合方法将作为当前使用的仿真方法的范式转移。
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element methods and custom loss functions from neural networks are merged to form the algorithm. The Finite Element Method-enhanced Neural Network hybrid model (FEM-NN hybrid) is data-efficient and physics conforming. The proposed methodology can be used for surrogate models in real-time simulation, uncertainty quantification, and optimization in the case of forward problems. It can be used for updating the models in the case of inverse problems. The method is demonstrated with examples, and the accuracy of the results and performance is compared against the conventional way of network training and the classical finite element method. An application of the forward-solving algorithm is demonstrated for the uncertainty quantification of wind effects on a high-rise buildings. The inverse algorithm is demonstrated in the speed-dependent bearing coefficient identification of fluid bearings. The hybrid methodology of this kind will serve as a paradigm shift in the simulation methods currently used.
