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목록전체 글 (41)
Mathematics & Computation
NTK만kL2 errorH1 error1 1.718e-031.694e-0221.563e-031.503e-0234.942e-035.287e-024 5.266e-011.986e+005 3.085e-01 1.747e+0061.811e-011.171e+00 71.137e-01 8.212e-0188.470e-02 6.915e-01 9 6.481e-025.693e-01104.688e-024.376e-01 NTK + curriculum kL2 errorH1 error11.712e-03 1.695e-022 6.404e-047.420e-033 5.349e-047.210e-0342.361e-031.132e-0252.143e-031.396e-026 1.219e-03 1.048e-0271.748e-03 1.513e-028..
model = PINN([2, 50, 50, 50, 1]).to(device)step = 20a1, a2 = 1,1 LAMBDA_BC = 1.0LAMBDA_PDE = 1.0LAMBDA_IC = 5.0 # anchor를 쓰는 경우 # 손실 총 스케일(항상 고정): 예시 60.0SUM_W = 60.0 1.K_SCHEDULE = [ (0, 1.0), (5000, 3.0), (10000, 6.0), (15000, 10.0),] L2 abs: 1.566e-02 | L2 rel: 1.566e-02 H1 abs: 1.632e-01 | H1 rel: 3.531e-02 L_inf abs:2.810e-02 2.K_SCHEDULE = [ (0, 1.0), (10000, 10.0),] L2 abs: 2.551e-02 |..
epoch = 20000model = PINN([3, 50, 50, 50,50, 1]).to(device)a1, a2 = 1, 1 k=1k=2k=3k=4k=5k=6step = 10Relative L2 error4.8791e-026.7382e-02 1.0356e-01 9.9476e-01 9.9869e-01 4.8525e-01Relative H1 error 5.2810e-024.2188e-029.2454e-029.9470e-01 9.9657e-01 5.2326e-01Time 2m2m2m3m3m3mstep = 20Relative L2 error1.0876e-01 4.5514e-02 2.4261e-01 9.0612e-01 6.0647e-01Relative H1 error 1.1269e-014.0538e..
#Try1: Max error: 2.1042e+00 Relative Error: 1.4976e+00 #Try2: #Try3:L-BGFS추가파일
Helmholtz Equ
model = PINN([2, 50,50,50, 1]).to(device)step = 50a1,a2 = 1,1k = pi * torch.sqrt(torch.tensor(a1**2 + a2**2, dtype=torch.float32, device=device)optimizer lr = 1e-3threshold loss = 1e-9 #Try1:epoch = 40000max error: 1.0238e-01 Relative Error: 8.9404e-02 #Try2:epoch 40000L-BFGS사용 Max error: 1.8156e-03 Relative Error: 7.2430e-04 #Try3:epoch = 30000 Max error: 1.2876e-02 Relative Error: 7.9915e-0..
SA-PINN+Fourier을 이용한 2차원 Poisson 방정식 해석 및 성능 향상 전략
class PINN(nn.Module): def __init__(self, in_dim=16, hidden=64, out_dim=1): super().__init__() self.net = nn.Sequential( nn.Linear(in_dim, hidden), nn.Tanh(), nn.Linear(hidden, hidden), nn.Tanh(), nn.Linear(hidden, out_dim) SA-PINN + Fourier #Try 1:collocation point = 100bounday point = 40 epochs = 10000 max error: 4.2092e-01 Relative Error: 2.6617e-014m (시간은 정확하지 않음) => Prediction은 Exact에 비해 파..
11
기본 설정a1 =2 , a2=2Model = [2,50,50,50,1]Lambda 1 = 100, Lambda 2 = 1a1,a2 = 2Epochstep4105010030050010000max abs Error3.99403e+002.0125e+001.9990e+00 2.0042e+001.99772+002.0072e+00relative Error9.3241e-01 4.9915e-014.9974e-015.0022e-014.9919e-015.0067e-01Time1m 1m1m1m9m 30000max abs Error4.0350e+00 2.0064e+00 1.9998e+002.0036e+002.0041e+00relative Error9.1490e-015.0030e-014.9995e-014.9990e-015.00..