(649b) Accelerating Multicomponent Phase-Coexistence Calculations with Physics-Informed Neural Networks

Phase separation in multicomponent mixtures is of significant interest in both fundamental research and technology [1-2]. Although the thermodynamic principles governing phase equilibria are straightforward, practical determination of equilibrium phases and their constituent compositions for multicomponent systems remains computationally intensive. Current multiphase calculation schemes often require prior knowledge of the number of equilibrium phases, are sensitive to initial guesses, and can converge to spurious solutions if not properly constrained [3-5]. While machine learning techniques have shown promise for phase-coexistence calculations, existing approaches largely address only phase stability without determining phase compositions or remain limited to binary systems with minimal demonstration in more complex mixtures [6-8].

In this talk, I will present a data-driven workflow to characterize phase behavior in multicomponent systems [9]. Using Flory–Huggins theory as a representative free-energy model, we generate ternary phase diagrams across parameter space and train a theory-aware machine learning model to predict the number, composition, and relative abundance of equilibrium phases from model parameters and total system composition. The model encodes fundamental physical laws (e.g., chemical potential equality, mass balance, and free energy minimization) into the architecture, enabling predictions that serve as initial guesses to warm-start subsequent numerical optimization. This hybrid approach, which combines physics-informed machine learning predictions with targeted optimization, matches the accuracy of traditional methods at significantly reduced computational cost. The framework is extensible beyond ternary systems and applicable to other free-energy models, offering a promising pathway to accelerate chemical process simulations and drive innovations in multi-phase separation technologies.

[1] Guillen, G. R., Pan, Y., Li, M. & Hoek, E. M. V. Preparation and Characterization of Membranes Formed by Nonsolvent Induced Phase Separation: A Review. Ind. Eng. Chem. Res. 50, 3798–3817 (2011).

[2] Molliex, A. et al. Phase Separation by Low Complexity Domains Promotes Stress Granule Assembly and Drives Pathological Fibrillization. Cell 163, 123–133 (2015).

[3] Peng, D.-Y. & Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 15, 59–64 (1976).

[4] Jindrová, T. & Mikyška, J. Fast and robust algorithm for calculation of two-phase equilibria at given volume, temperature, and moles. Fluid Phase Equilibria 353, 101–114 (2013).

[5] Tong, W., Xiong, W. & Zhan, Y. An initial value insensitive constrained linear predictive evolution algorithm for gas–liquid phase equilibrium calculation problems. Phys. Fluids 36, 083351 (2024).

[6] Terayama, K. et al. Acceleration of phase diagram construction by machine learning incorporating Gibbs’ phase rule. Scr. Mater. 208, 114335 (2022).

[7] Deffrennes, G., Terayama, K., Abe, T. & Tamura, R. A machine learning–based classification approach for phase diagram prediction. Mater. Des. 215, 110497 (2022).

[8] Thacker, J. C. R., Bray, D. J., Warren, P. B. & Anderson, R. L. Can Machine Learning Predict the Phase Behavior of Surfactants? J. Phys. Chem. B 127, 3711–3727 (2023).

[9] Dhamankar, S., Jiang, S. & Webb, M. A. Accelerating multicomponent phase-coexistence calculations with physics-informed neural networks. Mol. Syst. Des. Eng. 10, 89–101 (2024).