30 lines
926 B
Python
30 lines
926 B
Python
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import torch
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import torch.nn as nn
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#多元多项式拟合
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# 数据生成 (x1, x2 -> y)
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x1 = torch.rand(100, 1) * 4 - 2 # [-2, 2]
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x2 = torch.rand(100, 1) * 3 - 1 # [-1, 2]
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y_true = 2.7*x1 + 3.0*x2 + 5.0*x1*x2 - 1.5*x1**2*x2 # 真实多项式
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# 特征工程
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def make_features(x1, x2, degree=3):
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features = [torch.ones_like(x1)]
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for d in range(1, degree+1):
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for i in range(d+1):
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features.append((x1**i) * (x2**(d-i)))
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return torch.cat(features, dim=1)
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x_poly = make_features(x1, x2, degree=3)
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# 模型训练
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model = nn.Sequential(nn.Linear(10, 1)) # 3次多项式共10项
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optimizer = torch.optim.Adam(model.parameters(), lr=1e-3, weight_decay=0.1)
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for epoch in range(2000):
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y_pred = model(x_poly)
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loss = nn.MSELoss()(y_pred, y_true)
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optimizer.zero_grad()
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loss.backward()
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optimizer.step()
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if epoch % 500 == 0:
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print(f'Epoch {epoch}, Loss: {loss.item():.4f}')
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