As the finite element method requires many nodes or elements to obtain accurate results, the adaptive finite element method has been developed to obtain better results with fewer nodes, where error information is used to refine the initial mesh adaptively. In contrast to this, we propose in this paper two new methods to directly derive accurate results by artificial neural networks using information about the errors of analysis results. One of the proposed methods employs error information obtained using a posteriori error estimator to predict accurate solutions from a single analysis with a coarse mesh. The other utilizes error information obtained from comparison between two analysis results: analysis results by using a coarse mesh and those by using the corresponding refined mesh. In both methods above, the artificial neural network is employed to predict accurate results at any target point in the analysis domain based on the error information around the point. These methods are successfully tested in two-dimensional stress analyses.

由于有限元方法需要许多节点或元素才能获得准确的结果，因此已经开发了自适应有限元方法，以用更少的节点获得更好的结果，其中使用误差信息来自适应地优化初始网格。与此相反，我们提出了两种新方法，它们可以使用有关分析结果误差的信息，通过人工神经网络直接得出准确结果。所提出的方法之一是利用使用后验误差估计器获得的误差信息来预测粗网格的单次分析的精确解。另一个利用从两个分析结果之间的比较中获得的误差信息：使用粗糙网格的分析结果和使用相应细化网格的分析结果。在以上两种方法中，人工神经网络可根据该点周围的误差信息来预测该分析域中任意目标点的准确结果。这些方法已在二维应力分析中成功测试。