Knowledge graphs (KGs) are widely used for modeling scholarly communication, informing scientometric analysis, and supporting a variety of intelligent services to explore the literature and predict research dynamics. However, they often suffer from incompleteness (eg, missing affiliations, references, research topics), which ends up reducing the scope and quality of the resulting analysis. This issue is usually tackled by computing knowledge graph embeddings (KGEs) and applying link prediction techniques. However, only a few KGE models are capable of taking weights of facts in the knowledge graph into account. Such weights can have different meanings, eg describe the degree of association or the degree of truth. In this paper we propose Weighted Triple Loss, a new loss function for KGE models that takes full advantage of the additional numerical weights on facts. We also extend the Rule Loss, a loss function that is able to exploit a set of logical rules, in order to work with weighted triples. The evaluation of our solutions on several knowledge graphs indicates significant performance improvements with respect to the state of the art. Our main use case is the large-scale AIDA knowledge graph, which describes 21 million research articles. Our approach enables to complete information about affiliation types, countries, and research topics, greatly improving the scope of the resulting scientometrics analysis and providing better support to systems for monitoring and predicting research dynamics.