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Due to its rich and intuitive expressivity,knowledge graph has received much attention of many scholars. A lot of works have been accumulated in knowledge graph embedding. The results of the works have played an important role in some fields, such as e-commerce, finance,medicine, transportation and intelligent Q & A. In the knowledge graph embedding model, the loss function plays a key role in its training stage. Based on the existing research of knowledge graph embeddings, this paper classifies the loss functions used in the model into six categories: hinge loss, logistic loss, cross entropy loss, log likelihood loss, negative sampling loss and mean square error loss. The prototype formula and physical meaning of loss functions and their expansion, evolution and application in knowledge graph embedding models are analyzed in detail one by one.Based on the above,the usage, efficiency and convergence of various loss functions in the static and dynamic knowledge graph scenarios are comprehensively analyzed and evaluated. According to the analysis results, combined with the development and application trend of knowledge graph and the current situation of loss functions,the future works of loss functions are discussed.

Extensive research has been conducted on models of ordinary differential equations (ODEs), yet these deterministic models often fail to capture the intricate complexities of real-world systems adequately. Thus, many studies have proposed the integration of Markov chains into nonlinear dynamical systems to account for perturbations arising from environmental changes and random variations. Notably, the field of parameter estimation for ODEs incorporating Markov chains still needs to be explored, creating a significant research gap. Therefore, the objective of this study is to investigate a comprehensive model capable of encompassing real-life scenarios. This model combines a system of ODEs with a continuous-time Markov chain, enabling the representation of a continuous system with discrete parameter switching. We present a machine discovery framework for parameter estimation in nonlinear dynamical systems with Markovian switching, effectively addressing this research gap. By incorporating Markov chains into the model, we adeptly capture the time-varying dynamics of real-life systems influenced by environmental factors. This approach enhances the applicability and realism of the research, enabling more precise representations of dynamical systems with Markovian switching in complex scenarios., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)