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Abstract 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 labeled data needed to train the model. This poses severe challenges in data-scarce settings where obtaining labels requires substantial computational or labor resources. Noting that problems in natural sciences often benefit from easily obtainable auxiliary information sources, 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: abundant unlabeled data, prior knowledge of symmetries or invariances, and 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 Schrödinger equation. SIB-CL consistently results in orders of magnitude reduction in the number of labels needed to achieve the same network accuracies. 

Bioremediation of chlorinated aliphatic hydrocarbon-contaminated aquifers can be hindered by high contaminant concentrations and acids generated during remediation. Encapsulating microbes in hydrogels may provide a protective, tunable environment from inhibiting compounds; however, current approaches to formulate successful encapsulated systems rely on trial and error rather than engineering approaches because fundamental information on mass-transfer coefficients is lacking. To address this knowledge gap, hydronium ion mass-transfer rates through two commonly used hydrogel materials, poly(vinyl alcohol) and alginic acid, under two solidification methods (chemical and cryogenic) were measured. Variations in hydrogel crosslinking conditions, polymer composition, and solvent ionic strength were investigated to understand how each influenced hydronium ion diffusivity. A three-way ANOVA indicated that the ionic strength, membrane type, and crosslinking method significantly (p < 0.001) contributed to changes in hydronium ion mass transfer. Hydronium ion diffusion increased with ionic strength, counter to what is observed in aqueous-only (no polymer) solutions. Co-occurring mechanisms correlated to increased hydronium ion diffusion with ionic strength included an increased water fraction within hydrogel matrices and hydrogel contraction. Measured diffusion rates determined in this study provide first principal design information to further optimize encapsulating hydrogels for bioremediation.