## 2 Methods
### The NHLBVNet Model
#### 2.1.3 Combustion Feature Module  
The task of the combustion feature module is to thoroughly extract features from the input data, thereby providing support for the combustion prediction module to output precise results. The combustion feature module initially employs XGBoost [19] for preliminary feature extraction.  
XGBoost is an algorithm based on gradient boosting decision trees [20; 21]. Gradient boosting involves predicting the residuals or errors from previous models and then summing these to form the final prediction. It is referred to as gradient boosting because it employs the gradient descent algorithm [22; 23] to minimize the loss when introducing new models into the ensemble. XGBoost also enhances the interpretability of the model [24]. Compared to random forests, XGBoost is faster and more accurate, offering superior model performance. A significant amount of work has utilized XGBoost for tasks of feature selection and feature combination [25; 26; 27].  
Within the combustion feature module, the formula used for XGBoost is represented as Equation (1).  
\[y_{i}\ =\sum_{k=1}^{M}f_{k}(h_{i}) \tag{1}\]  
where \(h_{i}\) represents the combustion reaction information obtained from the ith experiment; XGBoost learns a base learner \(f_{k}\) for each feature, and then sums the outputs of all base learners as the predicted laminar burning velocity of the ammonia-hydrogen mixture, thereby conducting gradient boosting training.  
To further extract features, the combustion feature module employs a multi-layer perceptron [28] for preliminary feature learning of the data. As a classic machine learning method, the multi-layer perceptron is capable of fitting tasks while minimizing the loss of information [29]. Through the multi-layer perceptron, the model can obtain the combustion feature embedding vectors. The formula used in this stage is shown as Equation (2).  
\[e_{i}=Wh_{i}+b \tag{2}\]  
where \(e_{i}\) represents the combustion feature embedding vector obtained from the ith experiment; \(W\) represents the weight matrix; and \(b\) denotes the bias term.  
Subsequently, the combustion feature module employs a structure akin to residual neural networks [30] for information integration. Given the value of the data within the dataset, to enhance the model's capacity for learning the distribution of the original data, this research adds the outputs from the various base learners \(f_{k}(h_{i})\) in XGBoost to the combustion reaction information \(h_{i}\) obtained from the ith experiment. This approach strengthens the model's learning of the raw data. The formula used is shown as Equation (3).  
\[q_{i}=\alpha\circ f_{k}(h_{i})+(1-\alpha)\circ h_{i} \tag{3}\]  
where \(\alpha\) is a hyperparameter used to control the proportion of various data within the ResNet structure; \(f_{k}\) represents the decision tree obtained from the kth training iteration, with each \(f_{k}(h_{i})\) corresponding to an independent tree structure, where each \(f_{k}(h_{i})\) scores the sample \(h_{i}\). These scores are collected; the obtained scores are multiplied by the hyperparameter \(\alpha\) and added to the combustion reaction information to obtain the ith combustion feature vector \(q_{i}\).  
After processing through the combustion feature module, the model conducts comprehensive feature learning and integration of the combustion reaction information \(h_{i}\). The resulting combustion feature vector \(q_{i}\) will then be passed as the output of the combustion feature module to the subsequent module.