Helmholtz 2D

<2D Helmholtz 기본설정>

epoch = 20000

model = PINN([3, 50, 50, 50,50, 1]).to(device)

a1, a2 = 1, 1

 

		k=1	k=2	k=3	k=4	k=5	k=6
step = 10	Relative L2 error	4.8791e-02	6.7382e-02	1.0356e-01	9.9476e-01	9.9869e-01	4.8525e-01
	Relative H1 error	5.2810e-02	4.2188e-02	9.2454e-02	9.9470e-01	9.9657e-01	5.2326e-01
Time		2m	2m	2m	3m	3m	3m
step = 20	Relative L2 error	1.0876e-01	4.5514e-02	2.4261e-01	9.0612e-01		6.0647e-01
	Relative H1 error	1.1269e-01	4.0538e-02	2.1134e-01	9.0133e-01		6.2201e-01
Time		3m	3m	3m	3m		3m
step = 50	Relative L2 error	1.8508e-01	3.1980e-02	1.1006e-01	9.9727e-01
	Relative H1 error	1.7201e-01	3.6134e-02	9.8976e-02	9.9718e-01
Time			3m	3m	3m
step = 100	Relative L2 error	2.1221e-01	5.4855e-02	9.3617e-02	9.5283e-01
	Relative H1 error	1.5359e-01	4.7532e-02	8.6432e-02	9.5061e-01
Time		3m	3m	3m	3m

 

2D 수정

		k=1	k=2	k=3	k=4	k=5	k=6
step = 10	L2 abs	4.8791e-02	6.7382e-02	1.0356e-01	9.9476e-01	9.9869e-01	4.8525e-01
	H1 abs	5.2810e-02	4.2188e-02	9.2454e-02	9.9470e-01	9.9657e-01	5.2326e-01
	L_inf abs
Time		2m	2m	2m	3m	3m	3m
step = 20	L2 abs	1.0876e-01	4.5514e-02	2.4261e-01	9.0612e-01		6.0647e-01
	Relative H1 error	1.1269e-01	4.0538e-02	2.1134e-01	9.0133e-01		6.2201e-01
Time		3m	3m	3m	3m		3m
step = 50	L2 abs	1.8508e-01	3.1980e-02	1.1006e-01	9.9727e-01
	Relative H1 error	1.7201e-01	3.6134e-02	9.8976e-02	9.9718e-01
Time			3m	3m	3m

<3D Helmholtz 기본설정>

epoch = 20000

model = PINN([3, 50, 50, 50,50, 1]).to(device)

a1, a2, a3 = 1, 1, 1

 

		k=1	k=2	k=3	k=4	k=5	k=6	k=7	k=8
step = 10	Relative L2 error	4.3436 e-02	3.1329 e-02	1.1495 e-01	1.7946 e-01	1.4025 e+00	6.6732 e-01	2.2374 e-01	2.3602 e-01
	Relative H1 error	6.0832 e-02	4.6033 e-02	1.3077 e-01	1.7120 e-01	1.2487 e+00	7.2672 e-01	3.0964 e-01	3.5040 e-01
Time		5m	5m	5m	5m	5m	5m	5m	5m
step = 20	Relative L2 error	3.5939 e-02	3.1713 e-02	7.2913 e-02	1.2309 e+00	1.3994 e+00	5.9446 e-01	2.2844 e-01	2.0707 e-01
	Relative H1 error	5.4854 e-02	4.8447 e-02	9.7974 e-02	9.5947 e-01	1.2406 e+00	6.6353 e-01	3.2974 e-01	3.1934 e-01
Time		5m	5m	5m	5m	5m	5m	5m	5m

 

3D 수정

		k=1	k=2	k=3	k=4	k=5	k=6	k=7	k=8	k=9	k=10
step = 10	L2 abs	1.441e-02	1.431e-02	3.552e-02	6.587e-02	4.821e-01	2.080e-01	7.475e-02	8.162e-02	8.212e-02	7.422e-02
	L2 rel	4.076e-02	4.049e-02	1.005e-01	1.863e-01	1.364e+00	5.884e-01	2.114e-01	2.309e-01	2.323e-01	2.099e-01
	H1 abs	1.091e-01	9.796e-02	2.216e-01	3.048e-01	2.504e+00	1.380e+00	5.801e-01	7.271e-01	7.162e-01	6.674e-01
	H1 rel	5.411e-02	4.859e-02	1.099e-01	1.512e-01	1.242e+00	6.846e-01	2.877e-01	3.607e-01	3.552e-01	3.310e-01
	L_inf abs	5.917e-02	5.637e-02	1.245e-01	1.263e-01	1.270e+00	6.435e-01	2.428e-01	2.838e-01	3.112e-01	2.998e-01
step = 20	L2 abs	1.191e-02	9.701e-03	4.442e-02	2.014e-01	4.711e-01	2.361e-01	7.528e-02	7.796e-02	8.181e-02	6.834e-02
	L2 rel	3.369e-02	2.744e-02	1.257e-01	5.696e-01	1.332e+00	6.678e-01	2.129e-01	2.205e-01	2.314e-01	1.933e-01
	H1 abs	9.717e-02	8.384e-02	2.046e-01	7.907e-01	2.349e+00	1.496e+00	6.264e-01	6.376e-01	7.206e-01	6.058e-01
	H1 rel	4.820e-02	4.158e-02	1.015e-01	3.922e-01	1.165e+00	7.419e-01	3.107e-01	3.162e-01	3.574e-01	3.005e-01
	L_inf abs	6.422e-02	7.339e-02	2.110e-01	4.603e-01	1.203e+00	7.071e-01	2.433e-01	2.499e-01	3.473e-01	2.541e-01

 

 

2D 수정

		k=1	k=2	k=3	k=4	k=5	k=6	k=7	k=8	k=9	k=10
step = 10	L2 abs	1.242e-02	3.781e-02	6.394e-03	3.688e-02	2.534e-01	3.784e-01	1.353e-01	9.756e-02	6.400e-02	8.833e-02
	L2 rel	2.484e-02	7.563e-02	1.279e-02	7.376e-02	5.069e-01	7.567e-01	2.707e-01	1.951e-01	1.280e-01	1.767e-01
	H1 abs	8.016e-02	9.709e-02	4.372e-02	2.594e-01	1.397e+00	1.844e+00	8.348e-01	6.596e-01	4.755e-01	7.106e-01
	H1 rel	3.468e-02	4.201e-02	1.892e-02	1.123e-01	6.045e-01	7.979e-01	3.612e-01	2.854e-01	2.058e-01	3.074e-01
step = 20	L2 abs	2.793e-02	8.905e-02	1.481e-01	1.454e-02	1.430e-01	4.107e-01	1.698e-01	1.599e-01	1.036e-01	9.178e-02
	L2 rel	5.586e-02	1.781e-01	2.961e-01	2.907e-02	2.859e-01	8.213e-01	3.395e-01	3.198e-01	2.072e-01	1.836e-01
	H1 abs	1.356e-01	2.266e-01	6.018e-01	5.946e-02	7.544e-01	1.794e+00	8.975e-01	1.101e+00	6.774e-01	6.709e-01
	H1 rel	5.867e-02	9.806e-02	2.604e-01	2.573e-02	3.264e-01	7.763e-01	3.883e-01	4.762e-01	2.931e-01	2.903e-01