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.

翻译：我们提出吉布斯-杜亥姆约束神经网络，用于预测不同组成下二元混合物的活度系数。具体而言，我们在训练神经网络的损失函数中显式引入吉布斯-杜亥姆方程，这在支持自动微分的标准机器学习框架中可直接实现。与近期混合机器学习方法不同，本方法无需在神经网络内部嵌入特定热力学模型，从而避免了相应的预测局限性。相反，吉布斯-杜亥姆一致性作为正则化项，在保留机器学习模型灵活性的同时提升热力学一致性。实验结果表明，通过吉布斯-杜亥姆约束的图神经网络与矩阵补全方法，活度系数预测的热力学一致性与泛化能力均得到增强。我们还发现，模型架构（尤其是激活函数）对预测质量具有显著影响。该方法可便捷扩展至其他热力学一致性条件的约束场景。