Cultural heritage management poses significant challenges for museums due to fragmented data, limited intelligent frameworks, and insufficient applications. In response, a digital cultural heritage management approach based on knowledge graphs and deep learning algorithms is proposed to address the above challenges. A joint entity-relation triple extraction model is proposed to automatically identify entities and relations from fragmented data for knowledge graph construction. Additionally, a knowledge completion model is presented to predict missing information and improve knowledge graph completeness. Comparative simulations have been conducted to demonstrate the effectiveness and accuracy of the proposed approach for both the knowledge extraction model and the knowledge completion model. The efficacy of the knowledge graph application is corroborated through a case study utilizing ceramic data from the Palace Museum in China. This method may benefit users since it provides automated, interconnected, visually appealing, and easily accessible information about cultural heritage.