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 1 网格采样中对角线数据坐标的预测结果

Tab.1 Prediction results of diagonal data coordinates in grid sampling

$ x $ $ t $ 参数情况1 参数情况2 $ {R_{{\text{Pre}}}} $/10−1 $ {R_{{\text{Exa}}}} $/10−1 $ {E_{{\text{Abs}}}} $/10−3 $ {R_{{\text{Pre}}}} $/10−1 $ {R_{{\text{Exa}}}} $/10−1 $ {E_{{\text{Abs}}}} $/10−4 0.0 0.0 4.9957 5.0000 0.4296 7.0735 7.0711 2.4521 0.1 1.0 5.2330 5.2436 1.0540 8.5860 8.5756 10.3780 0.2 2.0 5.4697 5.4860 1.6249 9.4012 9.4095 8.2731 0.3 3.0 5.7092 5.7261 1.6925 9.7709 9.7750 4.0752 0.4 4.0 5.9568 5.9628 0.6045 9.9170 9.9172 0.2986 0.5 5.0 6.2043 6.1952 0.9111 9.9715 9.9700 1.5283 0.6 6.0 6.4406 6.4222 1.8459 9.9921 9.9892 2.9022 0.7 7.0 6.6602 6.6430 1.7280 10.0000 9.9961 3.8970 0.8 8.0 6.8613 6.8568 0.4469 10.0030 9.9986 3.9810 0.9 9.0 7.0435 7.0630 1.9533 10.0020 9.9995 2.7907 1.0 10.0 7.2075 7.2611 5.3639 10.0000 9.9998 0.2772