# Using a Machine Learning Method to Predict the Penetration Depth of a Gravity Core
## 5 Discussion
### Comparison of Different Penetration Depth Models  
To demonstrate the accuracy of the gravity sampler penetration depth machine learning model developed in this paper, three other t analytic solution models, defined as AS1 [9], AS2 [11], and AS3 [10], were used for computation and comparison. The 75 groups of gravity sampling data analyzed in this paper were computed using machine learning models and three other analytical solution models. The penetration depths calculated by the four models were analyzed in comparison to the actual penetration depths obtained using statistical methods (_MSE_, _MAE_, _EVS_, and \(R^{2}\)) mentioned in Section 3.2.  
The comparison results of the accuracy of different gravity sampling penetration depth prediction models are demonstrated in Table 3 and Figure 6. It well known that smaller _MSE_ and _MAE_ and larger _EVS_ and \(R^{2}\) values indicate more accurate prediction results. In terms of statistical metrics, the ML model yields the lowest _MSE_ and _MAE_ and the highest _EVS_ and \(R^{2}\) values. As for the other three analytic solution models, AS3 performs best on _MSE_, _MAE_, and _EVS_, and AS2 performs best on \(R^{2}\). Therefore, the accuracy of the four models is: ML > AS3 > AS2 > AS1. Moreover, the performance of the machine learning model is clearly and substantially ahead of that of the other analytical solution models.  
The prediction accuracy of machine learning models is much higher than that of various analytical solution models because the two computational methods employ very different processes. The traditional analytical solution model mainly analyzes the force of the gravity sampler penetration process, derives the energy of each component and process, and solves the equation according to energy conservation. This way of solving the energy conservation equation presents the following problems: (1) the calculation of each process is approximated, leading to the existence of certain errors; (2) there is a certain abbreviation in the calculation process, for example, AS2 does not consider the cutter head cutting work; and (3) because it involves sliding friction work between the sampling tube and the sediment, cutting work, and other processes, the calculation requires the estimation and approximation of the friction coefficient and other parameters, so it is difficult to calculate accurately. The machine learning model only needs to establish the numerical relationship between the input parameters and the penetration depth directly through continuous training and backpropagation based on the data, skipping the complex and extensive approximation process of various forces and energy calculations. Therefore, the prediction results of machine learning models are more accurate.  
In addition, because solving the energy conservation equation contains the physical meaning of numerous sampler penetration processes, many process parameters are required, such as the inner wall friction coefficient, outer wall friction coefficient, cutter head cutting coefficient, and other difficult-to-determine parameters. This status quo leads to numerous estimates for the modeling of the conventional analytical solution, which increases the complexity of the computational process and the error of the prediction results. In contrast, the machine learning model only requires a few critical influencing parameters to directly connect with the penetration depth. The computational parameters used in this model can be obtained before sampling. No parameter valuation is required, which significantly reduces the complexity of the model calculation and improves the prediction accuracy. Overall, the machine learning algorithm is superior to traditional analytical solution models in predicting the penetration depth of gravity samplers, both in terms of the accuracy of the model prediction results and the scientific nature of the computational process.