Molecules and materials are the foundation for the development of modern advanced industries such as energy storage systems and semiconductor devices. However, traditional trial-and-error methods or theoretical calculations are highly resource-intensive, and extremely long R&D (Research and Development) periods cannot meet the urgent need for molecules/materials in industrial development. Machine learning (ML) methods based on big data are expected to break this dilemma. However, the difficulty in constructing large-scale datasets of new molecules/materials due to the high cost of data acquisition and annotation limits the development of machine learning. The application of transfer learning lowers the data requirements for model training, which makes transfer learning stand out in researches addressing data quality issues. In this review, we summarize recent advances in transfer learning related to molecular and materials science. We focus on the application of transfer learning methods for the discovery of advanced molecules/materials, particularly, the construction of transfer learning frameworks for different systems, and how transfer learning can enhance the performance of models. In addition, the challenges of transfer learning are also discussed.

We systematically study some basic properties of the theory of pre-topological spaces, such as, pre-base, subspace, axioms of separation, connectedness, etc. Pre-topology is also known as knowledge space in the theory of knowledge structures. We discuss the language of axioms of separation of pre-topology in the theory of knowledge spaces, the relation of Alexandroff spaces and quasi ordinal spaces, and the applications of the density of pre-topological spaces in primary items for knowledge spaces. In particular, we give a characterization of a skill multimap such that the delineate knowledge structure is a knowledge space, which gives an answer to a problem in \cite{falmagne2011learning} or \cite{XGLJ} whenever each item with finitely many competencies; moreover, we give an algorithm to find the set of atom primary items for any finite knowledge spaces.