We compare the Finite Element Method (FEM) simulation of a standard Partial Differential Equation thermal problem of a plate with a hole with a Neural Network (NN) simulation. The largest deviation from the true solution obtained from FEM (0.025 for a solution on the order of unity) is easily achieved with NN too without much tuning of the hyperparameters. A higher accuracy value (0.001) instead requires refinement with an alternative optimizer to reach a similar performance with NN. A rough comparison between the Floating Point Operations values, as a machine-independent quantification of the computational performance, suggests a significant difference between FEM and NN in favour of the former. This also strongly holds for computation time: for an accuracy on the order of $10^{-5}$, FEM and NN require 38 and 1100 seconds, respectively. A detailed analysis of the effect of varying different hyperparameters shows that accuracy and computational time only weakly depend on the major part of them. Accuracies below 0.01 cannot be achieved with the "Adam" optimizers and it looks as though accuracies below $10^{-5}$ cannot be achieved at all. Training turns to be equally effective when performed on points extracted from the FEM mesh.

翻译：我们用神经网络模拟(NN)来比较板块标准局部分等热问题极量法模拟器(FEM),用神经网络模拟(NN)来比较标准部分分等热问题。从FEM(0.25用于统一等级的解决方案)获得的真正解决办法的最大偏差,也很容易与NNER(0.25用于统一等级的解决方案)相比,而无需对超光度计进行大量调整。提高精度值(0.001)则需要与NN(其他优化器)进行精细化,以便达到类似的性能。将浮动点操作值作为计算性能的机器独立量化方法,粗略地比较一下浮点操作值,表明FEM与N(NN)之间有显著的差别。这还强烈地维持在计算时间上:10 ⁇ -5美元(0.25美元)的准确度、FEM和NNN(NN)分别为38和1100秒。对不同的超光度计的影响进行详细分析后显示,精确性和计算时间仅取决于它们的主要部分。在“Adam”最优化时无法达到0.01的精确度,因为“Adam”优化,而且它看起来从10 5美元以下的精度从10美元到EM值不能完全实现。