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[分享]使用神经网络拟合数学函数v2
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发表于: 2025-2-5 18:35
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抱着学习的目的，让deepseekR1使用pytorch重写了以前文章《使用神经网络拟合数学函数》里的代码。真的不用自己写一行代码，就完美运行了，现在的AI太厉害了！
环境说明
torch_nn_fx.py
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | import torchimport torch.nn as nnimport torch.optim as optimclass RegressionNet(nn.Module): def __init__(self, input_dim, output_dim): super(RegressionNet, self).__init__() self.fc1 = nn.Linear(input_dim, 10) self.sigmoid1 = nn.Sigmoid() self.fc2 = nn.Linear(10, 10) self.sigmoid2 = nn.Sigmoid() self.fc3 = nn.Linear(10, output_dim) # 参数初始化 nn.init.normal_(self.fc1.weight) nn.init.normal_(self.fc1.bias) nn.init.normal_(self.fc2.weight) nn.init.normal_(self.fc2.bias) nn.init.normal_(self.fc3.weight) nn.init.normal_(self.fc3.bias) def forward(self, x): x = self.fc1(x) x = self.sigmoid1(x) x = self.fc2(x) x = self.sigmoid2(x) x = self.fc3(x) return xclass TorchFitFx: def __init__(self): self.model = None self.max_x = 1.0 self.max_y = 1.0 def _normalize(self, data, max_val): return torch.FloatTensor(data) / max_val def _denormalize(self, data, max_val): return data * max_val def _get_max_abs(self, tensor): return max(tensor.abs().max().item(), 1e-7) def train(self, X, Y, epochs=100000, lr=0.01): # 数据预处理 X_tensor = torch.FloatTensor(X) Y_tensor = torch.FloatTensor(Y) self.max_x = self._get_max_abs(X_tensor) self.max_y = self._get_max_abs(Y_tensor) X_normalized = X_tensor / self.max_x Y_normalized = Y_tensor / self.max_y # 初始化模型 input_dim = len(X[0]) # 修改这里 output_dim = len(Y[0]) # 修改这里 self.model = RegressionNet(input_dim, output_dim) criterion = nn.MSELoss() optimizer = optim.SGD(self.model.parameters(), lr=lr) # 训练循环 self.model.train() for epoch in range(epochs): optimizer.zero_grad() outputs = self.model(X_normalized) loss = criterion(outputs, Y_normalized) loss.backward() optimizer.step() if epoch % 10000 == 0: print(f"Epoch {epoch}, Loss: {loss.item():.6f}") if loss.item() < 0.0001: break def predict(self, X): if self.model is None: raise RuntimeError("Model not trained yet!") self.model.eval() with torch.no_grad(): X_tensor = torch.FloatTensor(X) X_normalized = X_tensor / self.max_x preds = self.model(X_normalized) return self._denormalize(preds, self.max_y).numpy()# 示例使用if __name__ == "__main__": def fx2(x): return (x - 5)**2 # 生成训练数据（确保X和Y都是二维列表） X = [[i] for i in range(0, 11)] # 二维列表 Y = [[fx2(x[0])] for x in X] # 二维列表 # 训练模型 fit_fx = TorchFitFx() fit_fx.train(X, Y, epochs=100000, lr=0.01) # 预测结果 test_points = [[i/2] for i in range(0, 21)] # 保持二维结构 predictions = fit_fx.predict(test_points) # 打印结果对比 print("\nPredictions vs Actual:") for x, pred in zip(test_points, predictions): actual = fx2(x[0]) print(f"x={x[0]:4.1f}, Predicted: {pred[0]:6.3f}, Actual: {actual:6.1f}") |
效果如下
torch_nn_fx_Sequential.py
让优化一下也能轻松搞定。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 | import torchimport torch.nn as nnimport torch.optim as optimclass RegressionNet(nn.Module): def __init__(self, input_dim, output_dim): super().__init__() self.net = nn.Sequential( nn.Linear(input_dim, 10), nn.Sigmoid(), nn.Linear(10, 10), nn.Sigmoid(), nn.Linear(10, output_dim) ) self._init_weights() def _init_weights(self): for layer in self.net: if isinstance(layer, nn.Linear): nn.init.normal_(layer.weight) nn.init.normal_(layer.bias) def forward(self, x): return self.net(x)class TorchFitFx: def __init__(self): self.model = None self.max_x = 1.0 self.max_y = 1.0 def train(self, X, Y, epochs=100000, lr=0.01): X_tensor = torch.as_tensor(X, dtype=torch.float32) Y_tensor = torch.as_tensor(Y, dtype=torch.float32) self.max_x = X_tensor.abs().max().clamp_min(1e-7) self.max_y = Y_tensor.abs().max().clamp_min(1e-7) X_normalized = X_tensor / self.max_x Y_normalized = Y_tensor / self.max_y self.model = RegressionNet(X_tensor.shape[1], Y_tensor.shape[1]) optimizer = optim.SGD(self.model.parameters(), lr=lr) criterion = nn.MSELoss() self.model.train() for epoch in range(epochs): optimizer.zero_grad() outputs = self.model(X_normalized) loss = criterion(outputs, Y_normalized) loss.backward() optimizer.step() if epoch % 10000 == 0 or loss < 0.0001: print(f"Epoch {epoch:5d}, Loss: {loss.item():.6f}") if loss < 0.0001: break def predict(self, X): if self.model is None: raise RuntimeError("Model not trained!") self.model.eval() with torch.no_grad(): X_tensor = torch.as_tensor(X, dtype=torch.float32) return self.model(X_tensor / self.max_x) * self.max_y# 示例使用if __name__ == "__main__": def fx2(x): return (x - 5)**2 # 生成训练数据（二维结构） X = [[i] for i in range(11)] Y = [[fx2(x[0])] for x in X] # 训练预测 fit_fx = TorchFitFx() fit_fx.train(X, Y, epochs=100000, lr=0.01) # 测试预测 test_points = [[i/2] for i in range(21)] predictions = fit_fx.predict(test_points) # 结果对比 print("\nPredictions vs Actual:") for x, pred in zip(test_points, predictions): print(f"x={x[0]:4.1f}, Predicted: {pred.item():6.3f}, Actual: {fx2(x[0]):6.1f}") |
效果如下
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最后于 2025-2-5 18:38
被Jtian编辑
，原因：
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