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Deep learning models are gaining popularity and potency in predicting polymer properties. These models can be built using pre-existing data and are useful for the rapid prediction of polymer properties. However, the performance of a deep learning model is intricately connected to its topology and the volume of training data. There is no facile protocol available to select a deep learning architecture, and there is a lack of a large volume of homogeneous sequence-property data of polymers. These two factors are the primary bottleneck for the efficient development of deep learning models. Here we assess the severity of these factors and propose new algorithms to address them. We show that a linear layer-by-layer expansion of a neural network can help in identifying the best neural network topology for a given problem. Moreover, we map the discrete sequence space of a polymer to a continuous one-dimensional latent space using a machine learning pipeline to identify minimal data points for building a universal deep learning model. We implement these approaches for three representative cases of building sequence-property surrogate models, viz., the single-molecule radius of gyration of a copolymer, adhesive free energy of a copolymer, and copolymer compatibilizer, demonstrating the generality of the proposed strategies. This work establishes efficient methods for building universal deep learning models with minimal data and hyperparameters for predicting sequence-defined properties of polymers.