# Deep Knowledge Tracing Integrating Temporal Causal Inference and PINN
## 4 Experiment
### Results and Discussion  
We compared TLPKT_PINN with several previous methods. For fair comparison, all these methods have been tuned to have the best performance.  
* BKT: Using the hidden Markov model and Bayesian inference methods, it is used to evaluate and predict the dynamic changes in students' mastery of knowledge points during the learning process.
* DKT: The model is based on a Recurrent Neural Network (RNN) and is used to dynamically track students' mastery of knowledge points. It analyzes students' interactive data, learns their knowledge status, and predicts their performance in future tasks.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **ASSIST2012** & **ASSISTChall** \\ \hline Number of students & 28,914 & 1600 \\ Number of knowledge concepts & 265 & 102 \\ Number of problems & 532,090 & 3142 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Information on the dataset.  
* DKVMN: This model defines a static matrix to store potential knowledge concepts and a dynamic matrix to update the corresponding knowledge states over time through read and write operations, using a memory network to obtain the interpretable student knowledge states.
* AKT: This uses two self-attention encoders to learn context-aware representations of exercises and answers; the knowledge evolution model is called the knowledge retriever, which utilizes attention mechanisms to retrieve knowledge obtained in the past that is relevant to the current exercise.
* LPKT: Modeling the learning gain during the learning process by capturing the difference between two consecutive learning units. The diversity of learning benefits is measured by students' relevant knowledge status and interval time. The learning gate is used to distinguish students' ability to absorb knowledge, and the forgetting gate is used to determine the decrease in students' knowledge over time.  
This article conducted experimental comparisons with these classic knowledge tracking models and their latest variants, using Area Under Curve (AUC) and Root Mean Square Error (RMSE) under the ROC curve to analyze the performance of the comparison models. For all datasets, we performed standard 5-fold cross validation on all models. Therefore, for each group, 80% of the students were divided into a training set and the remaining 20% were used as a testing set. We randomly initialized all parameters in a uniform distribution. We learned all hyperparameters on the training set and evaluated the test set using the model that performed best on the validation set. We added a dropout layer with a dropout rate of 0.2 to prevent overfitting. In our implementation, dk and de parameters are set to 128, and da is set to 50. The small positive value \(\gamma\) to enhance the Q-matrix was set to 0.03. The experimental results are shown in Table 2.  
It can be seen that as an improvement to the LPKT model, the TLPKT-PINN method in this paper performs better in both datasets compared to deep learning methods such as DKT, DKVMN, and DIKT-CI, which showed an increase of at least 5% in AUC values across three datasets. In addition, as an improvement of the LPKT model, TLPKT-PINN has increased the AUC values by at least 2.6% in both datasets. This improvement is due to its integration of temporal causal relationships between knowledge points and consideration of student performance prediction.