AbstractPredicting properties from a material’s composition or structure is of great interest for materials design. Deep learning has recently garnered considerable interest in materials predictive tasks with low model errors when dealing with large materials data. However, deep learning models suffer in the small data regime that is common in materials science. Here we develop the AtomSets framework, which utilizes universal compositional and structural descriptors extracted from pre-trained graph network deep learning models with standard multi-layer perceptrons to achieve consistently high model accuracy for both small compositional data (<400) and large structural data (>130,000). The AtomSets models show lower errors than the graph network models at small data limits and other non-deep-learning models at large data limits. They also transfer better in a simulated materials discovery process where the targeted materials have property values out of the training data limits. The models require minimal domain knowledge inputs and are free from feature engineering. The presented AtomSets model framework can potentially accelerate machine learning-assisted materials design and discovery with less data restriction.