Neural Network Function Approximation

After sufficient training, neural networks can effectively approximate various nonlinear functions, including but not limited to polynomial functions, exponential functions, logarithmic functions, and more. By adjusting the neural network's architecture and parameters (such as the number of hidden layers, neurons per layer, and activation functions like ReLU or sigmoid), we can further enhance approximation accuracy and precision. The training process involves implementing key components like defining the network structure using frameworks like TensorFlow or PyTorch, preparing appropriate datasets, selecting suitable loss functions (e.g., Mean Squared Error for regression tasks), and applying optimization algorithms (such as gradient descent or Adam). Through continuous training iterations and hyperparameter tuning (e.g., learning rate adjustment, batch size optimization), we can significantly improve the network's approximation capabilities, making it applicable to various real-world problems.