Machine learning (ML) methods have the potential to revolutionize materials design, due to their ability to screen materials efficiently. Unlike other popular applications such as image recognition or language processing, large volumes of data are not available for materials design applications. Here, we first show that a standard learning approach using generic descriptors does not work for small data, unless it is guided by insights from physical equations. We then propose a novel method for transferring such physical insights onto more generic descriptors, allowing us to screen billions of unknown compositions for Li-ion conductivity, a scale which was previously unfeasible. This is accomplished by using the accurate model trained with physical insights to create a large database, on which we train a new ML model using the generic descriptors. Unlike previous applications of ML, this approach allows us to screen materials which have not necessarily been tested before (i.e., not on ICSD or Materials Project). Our method can be applied to any materials design application where a small amount of data is available, combined with high details of physical understanding.