Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance for activity-coefficient modeling. However, extending such approaches to equilibrium data arising from an extremum principle, such as liquid-liquid equilibria, remains difficult. Here we present DISCOMAX, a differentiable algorithm for phase-equilibrium calculation that guarantees thermodynamic consistency at both training and inference, only subject to a user-specified discretization. The method combines discrete enumeration of feasible phase states with masked softmax aggregation in the backward pass, with the propagation of the true equilibrium state in the forward pass, using a straight-through gradient estimator to enable physics-consistent end-to-end learning of neural \gls{gE}-models. We show that this approach bears analogy to statistical thermodynamics, and we evaluate it on binary liquid-liquid equilibrium data where it outperforms existing surrogate-based methods, while offering a general framework for learning from different kinds of equilibrium data.

翻译：准确预测相平衡仍是化学工程的核心挑战。融入热力学结构的物理一致性机器学习方法近期在活度系数建模中展现出优异性能。然而，将此类方法推广至由极值原理决定的平衡数据（如液液相平衡）仍存在困难。本文提出DISCOMAX——一种可微的相平衡计算算法，该算法在训练和推理阶段均能保证热力学一致性（仅受用户指定的离散化条件约束）。该方法将可行相态的离散枚举与反向传播中的掩码softmax聚合相结合，在前向传播中传播真实平衡态，并采用直通梯度估计器实现神经gE模型的物理一致性端到端学习。我们证明该方法与统计热力学具有类比性，并在二元液液相平衡数据上评估其性能，结果表明该方法优于现有基于代理的方法，同时为从不同类型平衡数据中学习提供了通用框架。