# Signal Separation Based on Knowledge Representation
## 1 Introduction
[17] introduced a strategy for constructing seismic datasets and trained fully convolutional networks (FCNs) to separate P-waves and S-waves, investigating the generalization performance of deep learning methods. [PERSON] et al. [18] used deep learning methods to train neural networks using data samples to separate P/S wavefields from ground seismic multi-component data. While intelligent P-wave and S-wave separation methods eliminate the need for precise parameter dependency, simplifying the wavefield separation process, they typically rely on data-driven approaches, leading to poor interpretability and dependence on a large amount of high-quality data labels. [PERSON] et al. [19] introduced the MixIT method, a fully unsupervised audio separation technique. MixIT constructs training samples by blending existing audio mixtures and utilizes deep neural networks to separate them into latent sources, approximating the original mixture. MixIT demonstrates competitive performance in speech separation tasks and enables unsupervised adaptation and learning from large real-world datasets, providing an economically efficient solution for the audio separation domain. [PERSON] et al. 's utilization of unsupervised variational autoencoders yielded remarkable performance in separation experiments involving mixed MNIST handwritten digits and audio spectrograms [20]. Although machine learning has achieved significant success, data-driven supervised methods lack interpretability and overly rely on data samples, while unsupervised approaches require accurate and appropriate prior information tailored to specific problems. A potential solution is to combine neural networks with domain expertise, leading to the concept of knowledge-guided neural networks [21; 22; 23; 24]. [PERSON] et al. [25] integrated domain expertise into the loss function of neural networks, demonstrating its effectiveness in scenarios with scarce training data. [PERSON] et al. [26] proposed a physics-informed neural network framework for solving forward and inverse problems of various partial differential equations, offering a more general method for knowledge-guided neural networks. [PERSON] et al. [27] summarized strategies for integrating prior knowledge into machine learning, providing various ideas for knowledge-guided neural networks. [PERSON] et al. [28] introduced domain knowledge into deep neural networks and successfully applied it to geophysics, offering feasible solutions to various problems in seismology. Knowledge-guided neural networks enhance network interpretability and reduce the need for large data samples. [PERSON] et al. [29] constructed a knowledge-guided autoencoder network to improve P-wave and S-wave separation in seismic exploration, achieving enhanced separation performance. In previous studies [30; 31; 32], the velocity model inversion of geological structures could be achieved through a knowledge-guided recurrent neural network (RNN), resulting in a relatively accurate velocity model. Although knowledge-guided neural networks can alleviate data dependency, effective training still requires a sufficient amount of knowledge-filtered data to ensure reliable model performance. However, their typical application scenarios often involve partial differential equations related to the target signal. Real-world applications, however, cover a broad range of scenarios, and knowledge representation is not limited to the form of partial differential equations. Therefore, selecting an appropriate knowledge representation method based on the specific application scenario is crucial for effectively implementing signal separation using knowledge-guided networks. However, this selection process is inherently challenging, as different scenarios may require distinct forms of knowledge representation, ranging from analytical models such as partial differential equations to data-driven statistical representations.