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import numpy as np
import matplotlib.pyplot as plt
import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.model_selection import train_test_split
# Step 1: Create Synthetic Data
np.random.seed(42)
X = np.linspace(-10, 10, 1000)
y = 2.5 * X + np.random.normal(0, 2, X.shape) # Linear relation with noise
# Split into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
# Convert to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32).view(-1, 1)
y_train = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)
X_test = torch.tensor(X_test, dtype=torch.float32).view(-1, 1)
y_test = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)
# Step 2: Define and Train a Neural Network Model
class SimpleNN(nn.Module):
def __init__(self):
super(SimpleNN, self).__init__()
self.fc1 = nn.Linear(1, 10)
self.fc2 = nn.Linear(10, 1)
def forward(self, x):
x = torch.relu(self.fc1(x))
x = self.fc2(x)
return x
# Initialize model, loss function, and optimizer
model = SimpleNN()
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)
# Training loop
epochs = 500
losses = []
for epoch in range(epochs):
model.train()
optimizer.zero_grad()
outputs = model(X_train)
loss = criterion(outputs, y_train)
loss.backward()
optimizer.step()
losses.append(loss.item())
if (epoch + 1) % 50 == 0:
print(f'Epoch [{epoch+1}/{epochs}], Loss: {loss.item():.4f}')
# Step 3: Plot the Results
# Plot the synthetic data and the model's predictions
model.eval()
with torch.no_grad():
predicted = model(X_test).numpy()
plt.figure(figsize=(12, 6))
# Plot data and predictions
plt.subplot(1, 2, 1)
plt.scatter(X_test, y_test, label='Original data', alpha=0.5)
plt.scatter(X_test, predicted, label='Fitted line', alpha=0.5)
plt.title('Regression Results')
plt.xlabel('X')
plt.ylabel('y')
plt.legend()
# Plot training loss
plt.subplot(1, 2, 2)
plt.plot(losses)
plt.title('Training Loss')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.tight_layout()
plt.show()
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