# A Novel Aerodynamic Modeling Method Based on Data for Tiltrotor evtol
## 3 Data-Driven Modeling Methods
### Data-Driven Network Model Design  
The multilayer perceptron (MLP) is a type of feedforward neural network with a simple connectivity pattern. It comprises an input layer, one or more hidden layers, and an output layer. Each hidden layer contains multiple neurons [21]. The MLP operates by connecting each neuron in a layer to every neuron in the next layer with appropriate weights and biases. Input data propagate from the input layer to the output layer through forward propagation.  
Figure 3: Effect of rotor wake on wing lift of XV15 tiltrotor aircraft.  
The input data are received by the network through the input layer neurons. Each neuron in a hidden layer receives a weighted sum of signals from all neurons in the previous layer. This weighted sum is then passed through an activation function, such as sigmoid or ReLU, which introduces nonlinearity and enables the network to learn complex patterns. The output of the activation function becomes the output of that neuron and the input for neurons in the next layer. MLP calculates its error by comparing its predictions with the expected outputs using a loss function at the output layer. The error is then propagated backward through the network using backpropagation, which employs the chain rule to calculate the contribution of each weight to the error. The weights in each layer are then adjusted based on the error signal and a learning rate to minimize the overall error. The iterative process of forward pass, error calculation, and backpropagation with weight updates continues during training until the network achieves an acceptable level of performance [22].  
MLP networks can be used for multifunctional learning, including classification and regression tasks. MLP demonstrates proficient performance in handling multivariable nonlinear regression problems with its classic architecture [21]. The relationship between the dimensionless aerodynamic coefficients introduced in Section 2 is similar in structure to the MLP neural network and essentially belongs to multiple nonlinear regression. Therefore, this article introduces an MLP neural network based on the input-output and influence factors described in the Section 2. The hidden layer neurons represent the unique aerodynamic characteristics and state variables of the tiltrotor evtol. However, in these complex coupling relationships, some factors do not influence each other. Therefore, these unrelated neurons should not be connected. The MLP topology diagram for the unique aerodynamic characteristics of the tiltrotor evtol is obtained as Figure 4.  
Figure 4: The structure of the MLP network topology (connections between neurons are only partially displayed for reasons of clarity and comprehensibility).  
During network training, the structural parameters of the MLP are determined based on the coupling characteristics of aerodynamic features and their training effect. To achieve non-interconnected neurons, the weight of the corresponding connections in the weight matrix can be set to zero. This reflects the unique aerodynamic characteristics of the tiltrotor evtol.  
This article employs a network comprising multiple layers of neurons, each comprising a LeakyReLU activation function. The network is trained using the Adam optimizer to calculate the weights of the MLP neural network model. All of these components are implemented in Python code based on the PyTorch framework.