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 2 固定迭代次数下预测值绝对误差随神经网络规模变化的描述性统计

Tab.2 Descriptive statistic of absolute error of predicted values with scale of neural networks under a fixed epoch

$ {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{Tim}}}} $/101 L2N10 1.7252 1.5875 5.0858 3.6818 0.8563 L2N20 1.1476 0.5662 2.6179 2.1679 1.0698 L2N40 0.9774 0.5504 1.8555 1.6741 1.2882 L4N10 0.7521 0.5027 2.2651 1.6853 1.2023 L4N20 0.6586 0.3417 1.5532 1.2726 1.5605 L4N40 0.4815 0.3338 1.1123 0.9160 2.2252 L6N10 0.4890 0.3775 1.3585 1.0056 1.6617 L6N20 0.3286 0.1570 0.7378 0.6244 2.1818 L6N40 0.3082 0.1371 0.6828 0.5584 3.0004