Screening cascades with multi-fidelity outputs have a long-standing history in materials chemistry as well. For instance, Yang et al. have recently proposed a two-step approach to improve the predictions of the short circuit density and fill-factor by leveraging data from low-fidelity simulators. The first step in that approach relies on an unsupervised autoencoder to extract a compressed representation of microstructure images. The second step then leverages the learnt latent space embedding augmented with a low-fidelity label to train a surrogate model on the high-fidelity dataset. In contrast to our approach, transfer learning is done on images and not on graph-structured data, and the latent space embedding is learnt without supervision done via low-fidelity data points. Furthermore, a completely unsupervised approach is unlikely to translate to molecules, as such representations are difficult to use for propertybased downstream prediction tasks . Another interesting approach to multi-fidelity learning is the composite neural network by Meng and Karniadakis that aims to learn the parameters of inverse PDE (partial differential equation) problems with non-linearities. However, the approach is designed for problems where the correlation between low-and high-fidelity data is unknown, a case that is not generally encountered in drug discovery or quantum simulations. It has been applied in the context of PDEs with shallow and small neural networks and has only been evaluated on relatively small datasets (between 30, 000 and 45, 000 samples) with mainly uni-dimensional functions.