  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.
