工程变形观测的神经网络模型如何实现，C++代码

以下是一个简单的工程变形观测的神经网络模型的实现，使用C语言编写：

1. 首先定义输入数据和输出数据的结构体，以及神经网络的结构体：

typedef struct {
    double x; // 输入数据x
    double y; // 输入数据y
} input_data;

typedef struct {
    double z; // 输出数据z
} output_data;

typedef struct {
    double w1; // 第一层权重
    double w2; // 第二层权重
    double w3; // 第三层权重
} weights;

typedef struct {
    weights layer1; // 第一层权重
    weights layer2; // 第二层权重
} neural_network;

2. 定义激活函数和神经网络前向传播函数：

double sigmoid(double x) {
    return 1.0 / (1.0 + exp(-x));
}

output_data forward(input_data input, neural_network network) {
    double h1 = sigmoid(input.x * network.layer1.w1 + input.y * network.layer1.w2);
    double h2 = sigmoid(input.x * network.layer2.w1 + input.y * network.layer2.w2);
    double z = sigmoid(h1 * network.layer2.w3 + h2 * network.layer2.w3);
    output_data output = {z};
    return output;
}

3. 定义损失函数和反向传播函数：

double loss(output_data output, output_data target) {
    return pow(output.z - target.z, 2);
}

neural_network backward(input_data input, output_data output, output_data target, neural_network network, double learning_rate) {
    double h1 = sigmoid(input.x * network.layer1.w1 + input.y * network.layer1.w2);
    double h2 = sigmoid(input.x * network.layer2.w1 + input.y * network.layer2.w2);
    double z = sigmoid(h1 * network.layer2.w3 + h2 * network.layer2.w3);
    double delta = (output.z - target.z) * z * (1 - z);
    double d_w3 = delta * h2;
    double d_w4 = delta * h1;
    double d_h1 = delta * network.layer2.w3 * h1 * (1 - h1);
    double d_h2 = delta * network.layer2.w3 * h2 * (1 - h2);
    double d_w1 = d_h1 * input.x;
    double d_w2 = d_h1 * input.y;
    double d_w5 = d_h2 * input.x;
    double d_w6 = d_h2 * input.y;
    network.layer1.w1 -= learning_rate * d_w1;
    network.layer1.w2 -= learning_rate * d_w2;
    network.layer2.w1 -= learning_rate * d_w5;
    network.layer2.w2 -= learning_rate * d_w6;
    network.layer2.w3 -= learning_rate * d_w3;
    network.layer2.w4 -= learning_rate * d_w4;
    return network;
}

4. 最后，训练神经网络并测试其性能：

int main() {
    input_data input = {1.0, 2.0};
    output_data target = {0.75};
    neural_network network = {{0.1, 0.2}, {0.3, 0.4, 0.5, 0.6}};
    output_data output = forward(input, network);
    double cost = loss(output, target);
    network = backward(input, output, target, network, 0.1);
    output = forward(input, network);
    cost = loss(output, target);
    printf("Output: %f\n", output.z);
    return 0;
}