Predicting copolymer critical parameters with a theory-integrated neural network

The phase behavior of polymer solutions is essential for designing materials with targeted properties, but classical theories such as Flory-Huggins are limited by mean-field assumptions and often fail to capture sequence-specific effects. Here, we develop a machine learning framework to predict the critical temperature and critical volume fraction of copolymer sequences, combining neural networks (NNs) with physically motivated scaling relations in a theory-integrated neural network (TI-NN). Using grand canonical Monte Carlo simulations of 3351 model copolymer sequences in solvents of varying selectivity across diverse architectures, we show that a standard NN achieves reasonable accuracy, while a TI-NN significantly reduces prediction errors and enables robust extrapolation beyond the training set. Feature analysis reveals that solvent selectivity and sequence blockiness are the dominant determinants of copolymer critical parameters. Overall, our work demonstrates that embedding theoretical insights within machine learning models enhances both accuracy and interpretability for predictions of copolymer phase behavior.