# Research on Wellbore Trajectory Prediction Based on a Pi-GRU Model
## 3 Experiments and Analysis
### Multimodel Comparison  
To comprehensively evaluate whether the Pi-GRU model outperforms other mainstream models in the current task, we designed and conducted a series of systematic comparative experiments. In the experiment, we selected five representative models as comparison baselines, namely the traditional BP (back propagation) neural network, long short-term memory network (LSTM), gated recurrent unit (GRU), and the CNN-BiLSTM model combining convolutional neural network and bidirectional long short-term memory network. And the transformer model is based on the attention mechanism. All models were trained and tested on the same dataset to ensure the fairness of the experiments and the comparability of the results. In addition, to further verify the potential of the Pi-GRU model in practical engineering applications and evaluate its advantages over traditional mechanical models, we have also incorporated the classic method of the minimum curvature method into the comparative experiment system. As a traditional method widely used in wellbore trajectory calculation, the results of the minimum curvature method have clear physical significance and engineering background. Therefore, comparing it with the prediction results of the Pi-GRU model can more intuitively reflect the improvement of the deep learning model in terms of accuracy and robustness. The experimental results show that the Pi-GRU model outperforms the comparison model in multiple evaluation indicators, demonstrating stronger predictive ability and generalization performance. Figures 13 and 14, respectively, present the experimental results of the minimum curvature method and the CNN-BiLSTM model, serving as important references for comparison with the Pi-GRU model. By analyzing these results, we can more clearly identify the differences among various methods in terms of prediction accuracy and adaptability to complex data patterns, thereby providing strong support for subsequent model optimization and practical applications. The comparison results are shown in Table 4. The minimum curvature method, as a representative of the traditional mechanical model, has a variance of 0.23 for the dip angle and 0.64 for the azimuth angle between the predicted value and the actual value. However, the variance of the dip angle for the Pi-GRU model is 0.01, and that of the azimuth angle is 0.06. Thus, it can be seen that the Pi-GRU model has the advantages of smaller error and higher prediction accuracy compared to the traditional mechanical model. In the comparison between the LSTM model and the Pi-GRU model, the mean square error of the dip angle decreased from 0.09 in the LSTM model to 0.01, a reduction of 88.89%, and the mean square error of the azimuth angle decreased from 0.34 to 0.06, a reduction of 82.35%. Even when facing emerging models like CNN-BiLSTM, it still shows significant advantages. Compared with the single-input model, the Pi-GRU model incorporates geological information, and its performance has been significantly improved. This finding indicates that introducing geological information enables the model to effectively reduce the trajectory drift error caused by geological condition changes (such as sudden changesin rock properties), allowing the model to more accurately capture the potential factors affecting the trajectory during the drill bit's drilling process. Figure 14: Results of the CNN-BiLSTM experiment. Figure 13: The experimental results of the minimum curvature method. Although the memory usage of Pi-GRU is relatively high, this resource consumption is reasonable compared with its significantly improved prediction accuracy. The training time reflects the learning efficiency and deployment feasibility of the model. The training time of Pi-GRU is 3.89 s, slightly longer than that of GRU (3.21 s) and CNN-BiLSTM (3.26 s). Considering that Pi-GRU can achieve higher prediction accuracy during the training process, its slightly longer training time is acceptable.