# Deep Knowledge Tracing Integrating Temporal Causal Inference and PINN
## 2 Related Work  
### Knowledge Tracing  
Knowledge tracing is a well-known problem in AI for education, consisting of monitoring how the knowledge state of students changes during the learning process and accurately predicting their performance in future exercises [9]. Knowledge tracing can be traced back to the late 20 th century, with [PERSON] and [PERSON] (1995) [4] proposing BKT. BKT uses a HMM to treat students' knowledge states as hidden variables and predicts the next state based on a state transition matrix. The BKT model primarily relies on four parameters: the probability that a student has mastered the knowledge point before answering questions related to it; the probability that the student will transition from not mastering to mastering the knowledge point on their next attempt; the probability that the student has mastered the knowledge point but answers related questions correctly (the guessing probability); and the probability that the student has mastered the knowledge point but answers incorrectly (the slipping probability). Based on these four parameters, the model can further characterize the student's response to the next question using conditional probabilities. Subsequently, BKT has a lot of extensions. [PERSON] et al. [10] proposed the Dynamic Bayesian Knowledge Tracing (DBKT) model, which utilizes Dynamic Bayesian Networks (DBNs) to capture the dynamic changes in students' knowledge states during the learning process, then leading to more accurate student modeling and personalized education. [PERSON] et al. [11] introduced the Three-Learning-State BKT (TLS-BKT) model, which divides the learning process into three states through an evaluation function. This model improves the binary node states in the BKT model, transforming the original \"not mastered/mastered\" states into \"not mastered/learning/mastered\" states, enhancing the model's flexibility and robustness. In recent years, an increasing number of researchers have introduced the deep learning into knowledge tracing to enhance its expressiveness and performance. A typical model based on deep learning is DKT proposed by [PERSON] et al. RNNs based on long short-term memory (LSTM), These networks can learn sequences of observations, thus causing the model to be well suited for time series applications [12]. DKT was the first to apply deep learning to knowledge tracing, allowing it to capture more complex student knowledge states without the need for explicit manual encoding of knowledge domains. It uses an RNN as a hidden unit to generate knowledge state vectors that represent students' knowledge states, and it outputs predicted student responses through a sigmoid linear layer. The LSTM mechanism, with its inherent \"gate\" design, can effectively extract the features and correlations of multiple time sequences [13]. Due to the interpretability issues of inputs and outputs, deep learning knowledge tracing has seen numerous improved models. For example, the Dynamic Key-Value Memory Network (DKVMN) [14] incorporates an attention mechanism, allowing it to utilize the relationships between foundational concepts and directly output students' mastery levels for each concept. Graph-based Knowledge Tracing (GKT) [15] is a knowledge tracing method based on graph neural networks, aimed at capturing the complex relationships between knowledge by constructing knowledge graphs and leveraging the powerful representation learning capabilities of graph neural networks to model students' learning processes. The Context-aware Attentive Knowledge Tracing (AKT) [16] model constructs context-aware representations of questions and an swers, using a monotonic attention mechanism to summarize students' past performances over time scales and employing the Rasch model to capture individual differences among questions covering the same concept. At present, deep learning technology has achieved state-of-the-art results in the processing of Euclidean data [17]. [PERSON] et al.