Gibbs–Duhem-informed neural networks for binary activity coefficient prediction

We propose Gibbs–Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. That is, we include the Gibbs–Duhem equation explicitly in the loss function for training neural networks, which is straightforward in standard machine learning (ML) frameworks enabling automatic differentiation. In contrast to recent hybrid ML approaches, our approach does not rely on embedding a specific thermodynamic model inside the neural network and corresponding prediction limitations. Rather, Gibbs–Duhem consistency serves as regularization, with the flexibility of ML models being preserved. Our results show increased thermodynamic consistency and generalization capabilities for activity coefficient predictions by Gibbs–Duhem-informed graph neural networks and matrix completion methods. We also find that the model architecture, particularly the activation function, can have a strong influence on the prediction quality. The approach can be easily extended to account for other thermodynamic consistency conditions.