Clapeyron Neural Networks for Single-Species Vapor-Liquid Equilibria

Accurate prediction of vapor--liquid equilibrium (VLE) for hydrocarbon-nitrogen mixtures remains challenging for cubic equations of state, particularly across broad ranges of composition and hydrocarbon chain length. While deep learning models can provide accurate predictions, they often lack interpretability and explicit analytical expressions. In this work, we propose a symbolic machine learning approach to discover interpretable symbolic corrections to Peng-Robinson equation-of-state (PR-EOS) predictions from experimental data. The proposed approach adopts a two-level strategy: symbolic expressions are first identified for individual hydrocarbon systems, after which their coefficients are represented as functions of carbon number to enable accurate prediction across different hydrocarbon systems. The results demonstrate significantly improved prediction accuracy over the original PR-EOS across all hydrocarbon-nitrogen systems. Overall, the proposed approach provides an interpretable symbolic correction framework for improving PR-EOS predictions of hydrocarbon-nitrogen VLE.

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.

MultiPUFFIN is a domain-informed multimodal foundation model for predicting thermophysical properties of small molecules, addressing a critical gap in chemical engineering, drug discovery, and materials science. Existing molecular foundation models pretrain on millions of molecules to learn general-purpose representations, but their standard MLP output layers impose no physical constraints, vapor pressure predictions may violate monotonic temperature dependence, and viscosity curves may lack the functional form required by process simulators. Domain-informed approaches that guarantee thermodynamic consistency have remained limited to single properties and small datasets, whereas multimodal foundation models have focused on biological activity rather than thermophysical properties. MultiPUFFIN fills this gap by fusing SMILES sequences, 2D molecular graphs, and 3D conformer geometries through bidirectional cross-modal attention and gated fusion, supplemented by auxiliary encoders for experimental conditions and molecular descriptors. The backbone is pretrained on 500,000 unlabelled PubChem molecules using three complementary self-supervised objectives. A condition-aware refinement stack of five conditioners (temperature, pH, pressure, polymorph, and measurement method) routes each property to a four-head tournament that selects the best-performing thermodynamically informed head for that property. MultiPUFFIN achieves a mean test R2 of 0.784 and outperforms fine-tuned ChemBERTa-2 on all nine properties despite training on roughly 2,000x fewer labeled molecules.