input: Write a function to create a Python system for generating natural language responses using a neural network model. The function should define an input layer, an embedding layer, a GRU layer, a dense output layer, compile the model, and train it. Then, it should generate a response to a specified utterance.
  
  assert generate_response("What time is it?")== ### Expected output based on the trained model
  assert generate_response("How are you?")== ### Expected output based on the trained model
  assert generate_response("What is the weather today?")== ### Expected output based on the trained model
output: def generate_response(utterance):
      import tensorflow as tf
      from tensorflow.keras.models import Sequential
      from tensorflow.keras.layers import Embedding, GRU, Dense
  
      # Define the model
      model = Sequential()
      model.add(Embedding(input_dim=10000, output_dim=64, input_length=10))
      model.add(GRU(128, return_sequences=True))
      model.add(GRU(64))
      model.add(Dense(64, activation='relu'))
      model.add(Dense(1, activation='linear'))
  
      # Compile the model
      model.compile(optimizer='adam', loss='mean_squared_error')
  
      # Train the model (for demonstration purposes, we'll use dummy data)
      model.fit(tf.random.uniform((100, 10), maxval=10000, dtype=tf.int64), tf.random.uniform((100, 1)), epochs=1)
  
      # Generate a response
      response = model.predict(tf.constant([utterance], dtype=tf.string))
      return response[0][0].numpy()