Accelerating Multicomponent Phase-Coexistence Calculations with Physics-informed Neural Networks

Phase separation in multicomponent mixtures is of significant interest in both fundamental research and technology. Although the thermodynamic principles governing phase equilibria are straightforward, practical determination of equilibrium phases and constituent compositions for multicomponent systems is often laborious and computationally intensive. Here, we present a machine-learning workflow that simplifies and accelerates phase-coexistence calculations. We specifically analyze capabilities of neural networks to predict the number, composition, and relative abundance of equilibrium phases of systems described by Flory-Huggins theory. We find that incorporating physics-informed material constraints into the neural network architecture enhances the prediction of equilibrium compositions compared to standard neural networks with minor errors along the boundaries of the stable region. However, introducing additional physics-informed losses does not lead to significant further improvement. These errors can be virtually eliminated by using machine-learning predictions as a warm-start for a subsequent optimization routine. This work provides a promising pathway to efficiently characterize multicomponent phase coexistence.