Surrogate- and invariance-boosted contrastive learning for data-scarce applications in science.

Deep learning techniques have been increasingly applied to the natural sciences, e.g., for property prediction and optimization or material discovery. A fundamental ingredient of such approaches is the vast quantity of labelled data needed to train the model; this poses severe challenges in data-scarce settings where obtaining labels requires substantial computational or labor resources. Here, we introduce surrogate- and invariance-boosted contrastive learning (SIB-CL), a deep learning framework which incorporates three ``inexpensive'' and easily obtainable auxiliary information sources to overcome data scarcity. Specifically, these are: 1)~abundant unlabeled data, 2)~prior knowledge of symmetries or invariances and 3)~surrogate data obtained at near-zero cost. We demonstrate SIB-CL's effectiveness and generality on various scientific problems, e.g., predicting the density-of-states of 2D photonic crystals and solving the 3D time-independent Schrodinger equation. SIB-CL consistently results in orders of magnitude reduction in the number of labels needed to achieve the same network accuracies.