## 3 Models Overview
### Marine-Predators-Algorithm-Based Random Forest  
While the traditional machine learning models mentioned above have shown certain advantages in determining the SOM content, they often require significant computational resources to search for optimal parameters and often fail to find the best hyperparameters. Therefore, we propose Marine-Predators-Algorithm-Based Random Forest (MPARF) to enhance the performance and training speed of the RF model while reducing model overfitting. Specifically, due to the significant impact of the number of trees (ntree) and the maximum depth of trees (mdepth) on the accuracy of RF model, this study utilizes the MPA to optimize the parameters ntree and mdepth. The MPARF model is constructed to enhance the performance of RF in SOM content detection. The MPA [23] is a novel metaheuristic optimization algorithm inspired by the behavior of marine predators. This algorithm mimics the predatory behavior and collective cooperation strategies observed in the ocean. The underlying concept of the MPA is to perform an optimization search by simulating the interactions between predators and prey in the ocean ecosystem. In the algorithm, the predators represent the candidate solutions in the search space, while the prey represents the optimal or local optimal solution of the problem. The optimization process of the MPA can be summarized as follows:  
(1) Initialization stage: The MPA initiates the optimization process by initializing the positions of prey in the search space, as described by the following theoretical formula:  
\[X_{0}=X_{\text{min}}+\text{rand}(X_{\text{max}}-X_{\text{min}}), \tag{3}\]  
where \(X_{\text{max}},X_{\text{min}}\) is the search space range, and \(\text{rand}()\) is random number from 0 to 1. (2) Optimization stage of MPA: The optimization stage consists of three scenarios that consider different velocity ratios and simulate the entire lifecycle of predators and prey. The first scenario occurs when the velocity ratio is high or when the prey's movement speed is higher than that of the predators. This situation occurs in the early iterations of the optimization process, when global search is crucial. In this stage, the optimal strategy for the predators is to maintain their current positions. The theoretical formula for the optimization process based on exploration strategy is as follows:  
\[ \begin{array}{c}\text{stepsize}_{i}=R_{\text{B}}\otimes(\text{Elite}_{i}-R _{\text{B}}\otimes\text{Prey}_{i}),\\ \text{Prey}_{i}=\text{Prey}_{i}+\text{P}\cdot\text{R}\otimes\text{stepsize}_{i },\\ \text{Iter}<\frac{1}{3}\text{MaxIter},\end{array}  \tag{4}\]  
where \(i=1,\ldots n\), stepsize is the movement step size for this stage, \(R_{\text{B}}\) is a Brownian walk random vector with normal distribution, and \(\otimes\) represents the element-wise multiplication operator. This symbol simulates the movement of the prey. P is 0.5. R is a randomly and uniformly distributed value within the range [0, 1]. Elite is an elite matrix composed of top-level predators. Iter is the current iteration number. MaxIter is the maximum number of iterations. The second case is when the speed ratio is unified or when the predators and prey move at almost the same speed. This situation occurs during the middle phase of optimization iterations, where the population is divided into two parts. The prey in the algorithm performs Levy flights to explore the search space, while the predators perform Brownian motion to explore, develop, and exploit the search space.