## 1 Introduction
Sometimes, in order to make the modeled channel model more concise and practical, deterministic channel modeling methods may have certain trade-offs and idealization of the parameters that affect the channel during modeling. Therefore, some scholars use statistical modeling methods for channel modeling. Statistical channel modeling uses a measurement platform to measure channel data in actual application scenarios and fits the actual data to obtain the empirical distribution and statistical characteristics of each channel parameter. Finally, the channel is reconstructed based on statistical characteristics. He et al. [6] conducted channel measurements from 220 GHz to 340 GHz using a vector network analyzer and proposed a propagation channel model for the terahertz band. It is represented by a logarithmic model:  
\[\alpha_{\text{trans}}=20\lg\left(\frac{c}{4\pi f}\right)-A_{PET}-20\lg(d) \tag{1}\]  
According to the measurement results, it was found \(A_{PET}=1.97\)dB. Traditional statistical methods rely on manually constructing mathematical channel model from data, which is time-consuming. In order to solve this problem, some researchers use neural networks to directly fit the channel model. On the one hand, for the existing wireless channel models, it is only necessary to train the neural network with the data generated by the corresponding models, so that the neural network can approximate the actual channel model under the minimum mean square error criterion. On the other hand, for wireless channels without channel models, neural network-based channel modeling uses measured data for training and does not need to determine the propagation path of electromagnetic waves, so it is not constrained by the environment and is more suitable for various complex scenarios. When the actual wireless channels are nonlinear/non-stationary, neural networks have a good performance in simulating nonlinear systems. Neural networks can train high-dimensional nonlinear data, and solve many problems that are difficult to be solved by traditional modeling methods. [PERSON] et al. [7] proposed a 3D MIMO indoor channel modeling method targeting the millimeter wave frequency band. Based on the convolutional neural network model, the input data are the coordinates of the transmitter and receiver, and the output characteristic parameters include the received power, delay, transmission azimuth, transmission elevation, arrival azimuth, and arrival elevation. [PERSON] et al. [8] used neural networks to improve the prediction of outdoor signal strength in the ultra-high frequency (UHF) band. The diffraction loss and transmitted signal strength are fed into the neural network and the strength of the received signal will be output at the output layer. The results show that the neural networks can improve the prediction of outdoor signal strength in the UHF band. However, these methods of using neural networks as a channel model make it difficult to reveal the mathematical characteristics and physical mechanism of the channel because of the interpretability issue of neural networks. [PERSON] et al. [9] noted the interpretability issue of using neural networks as a channel model and proposed a scheme to use causal neural networks for channel modeling. However, this method still uses neural networks directly as the channel model, although it enhances the interpretability of neural networks, it is not intuitive enough. In order to solve the problem of insufficient interpretability of neural network channels, [PERSON] et al. [10] first used channel data to train the neural networks as a channel model, and then used a genetic algorithm to generate a symbolic regression formula from the neural network channel model. This is the indirect use of the symbolic regression method to generate the channel model. This indirection may be unnecessary. Given the analysis of the above factors, this paper proposes a transformer symbolic regression-based inter-satellite terahertz channel modeling method which is based on the symbolic regression method PhySO [11].