基于物理信息神经网络的Burgers-Fisher方程求解方法

徐健,朱海龙,朱江乐,李春忠

Solution approach of Burgers-Fisher equation based on physics-informed neural networks

Jian XU,Hai-long ZHU,Jiang-le ZHU,Chun-zhong LI

表 3 固定训练时间下预测值绝对误差随神经网络规模变化的描述性统计

Tab.3 Descriptive statistic of absolute error of predicted values with scale of neural networks under a fixed training time

$ {S_{{\text{Net}}}} $ $ {E_{{\text{Max}}}} $/10−2 $ {E_{{\text{Min}}}} $/10−6 $ {E_{{\text{Mea}}}} $/10−3 $ {E_{{\text{Sta}}}} $/10−3 $ {T_{{\text{Num}}}} $/102 L2N10 1.3816 1.5199 4.0196 2.9153 11.7200 L2N20 1.3958 1.1166 3.0385 2.5699 9.3000 L2N40 1.2500 0.9080 2.9150 2.3720 6.6600 L4N10 1.0755 0.8524 3.3827 2.4212 8.4700 L4N20 0.8338 0.8027 2.3934 1.7815 6.7100 L4N40 0.9156 0.6179 2.4211 1.8794 5.0600 L6N10 0.8874 1.3987 2.8323 2.0030 6.2000 L6N20 0.6949 0.5106 2.2007 1.5836 4.8400 L6N40 0.8039 0.7987 2.1866 1.6607 3.5000