Physics-Embedded Machine Learning Model for Phase Equilibrium Prediction in Multicomponent Systems

We present TeNNet-SAC (<b>T</b>hermodynamics-<b>e</b>mbedded <b>N</b>eural <b>Net</b>work for <b>S</b>egment <b>A</b>ctivity <b>C</b>oefficient) model, a novel machine learning framework for predicting activity coefficients in liquid mixtures using only the SMILES representations of the constituent molecules. Inspired by the quantum chemistry-based COSMO-SAC model, TeNNet-SAC evaluates activity coefficients by summing contributions from molecular surface segments. The model comprises three core components: (1) a σ-profile predictor, which generates molecular fingerprints (i.e., surface segment charge histogram or σ-profile) directly from SMILES; (2) a geometry predictor, which estimates molecular volume and surface area from SMILES; and (3) a Γ predictor, which computes the activity coefficients of surface segments in solution. The σ-profile and geometry predictors are trained on 39,745 quantum solvation calculations. The Γ predictor is initially pretrained on one million synthetic data points to capture physically consistent behavior and is subsequently fine-tuned end-to-end using experimental activity coefficient data to improve predictive accuracy. The base TeNNet-SAC model achieves accuracy comparable to COSMO-SAC, while the fine-tuned version consistently outperforms COSMO-SAC across benchmark systems. By treating segment activity coefficients as intermediate variables, TeNNet-SAC naturally generalizes to multicomponent mixtures and satisfies thermodynamic consistency, offering a robust and scalable solution for activity coefficient prediction.