Nonlinear Fitting Using BP Neural Networks

Backpropagation (BP) Neural Network is a widely used feedforward neural network for handling nonlinear fitting problems. It employs the Backpropagation algorithm to adjust network weights, enabling modeling of complex nonlinear relationships. The neural network can be viewed as a black-box model since it establishes mappings between inputs and outputs through extensive data training and internal parameter adjustments, without requiring explicit mathematical expressions.

In system modeling, BP neural networks can approximate highly nonlinear relationships between inputs and outputs by learning patterns from training data. Its core mechanism involves two phases: forward propagation and backward propagation. Forward propagation computes predicted outputs using weighted sums and activation functions (e.g., sigmoid or ReLU), while backward propagation minimizes prediction errors by updating weights and biases through gradient descent. This makes BP networks particularly suitable for prediction tasks like time series forecasting and regression analysis.

Compared to traditional linear regression or polynomial fitting, BP neural networks automatically adapt to complex function forms without presuming data distributions. However, overfitting risks require mitigation through techniques like regularization (e.g., L2 penalty in loss functions) or cross-validation during training loops. Code implementations typically involve defining network architecture (layers/neurons), initializing weights, iterating through epochs, and calculating gradients via chain rule derivatives.