(207c) Thermodynamic Surrogate Modeling for Open-Source Pharmaceutical Process Simulations

Computational efficiency is a significant challenge in pharmaceutical process simulations, where accurate thermodynamic models are needed for drug formulation, purification, and separation processes [1,2]. However, evaluating complex thermodynamic models can be computationally expensive, limiting their use in large-scale simulations. This work presents a hybrid modeling framework that integrates Gaussian process (GP)-based thermodynamic surrogate models into process simulations, addressing this challenge. Our contributions span software integration by linking open-source tools to enhance process simulation capabilities and methodological advancements through improved surrogate modeling strategies.

Regarding software, we developed a GP surrogate for activity coefficient predictions in a water-ethanol mixture as a case study. The surrogate was embedded in a distillation process modeled using PharmaPy [3], an open-source process simulation tool widely used in pharmaceutical modeling. A key innovation of this work is the linking of PharmaPy with Clapeyron.jl [4], a high-performance thermodynamic library implemented in Julia. This connection enables PharmaPy to incorporate custom thermodynamic models, improving its flexibility for pharmaceutical process simulations. This study demonstrates this capability using SAFT-γ Mie [5], a thermodynamic model that employs statistical associating fluid theory (SAFT) [6,7,8] with Mie potentials to accurately describe phase behavior and intermolecular interactions in complex fluid systems. This integration is a stepping stone toward embedding a broader range of thermodynamic models into PharmaPy for pharmaceutical unit operations.

Regarding methodology, we employed maximum entropy model-based design of experiments (MBDOE) [9,10] to systematically construct the GP surrogate model, ensuring that the most informative thermodynamic states were sampled. A key contribution of this work is the derivation of a closed-form information-theoretic acquisition function, enabling efficient Bayesian optimization of hierarchical GP models [11]. This approach optimized the surrogate model’s accuracy while minimizing data requirements, ultimately enhancing its effectiveness in process simulations.

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[4] Walker, P. J., Yew, H.-W., & Riedemann, A. (2022). Clapeyron.jl: An extensible, open-source fluid thermodynamics toolkit. Industrial & Engineering Chemistry Research, 61(20), 7130–7153. https://doi.org/10.1021/acs.iecr.2c00326

[5] Papaioannou, V., Lafitte, T., Avendaño, C., Adjiman, C. S., Jackson, G., Müller, E. A., & Galindo, A. (2014). Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments. Journal of Chemical Physics, 140(5), 054107. https://doi.org/10.1063/1.4851455

[6] Chapman, W. G., Jackson, G., & Gubbins, K. E. (1988). Phase equilibria of associating fluids: Chain molecules with multiple bonding sites. Molecular Physics, 65(5), 1057–1079. https://doi.org/10.1080/00268978800101601

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[8] Chapman, W. G., Gubbins, K. E., Jackson, G., & Radosz, M. (1990). New reference equation of state for associating liquids. Industrial & Engineering Chemistry Research, 29(8), 1709–1721. https://doi.org/10.1021/ie00104a021

[9] Shewry, M. C., & Wynn, H. P. (1987). Maximum entropy sampling. Journal of Applied Statistics, 14(2), 165–170. https://doi.org/10.1080/02664768700000020

[10] Currin, C., Mitchell, T., Morris, M., & Ylvisaker, D. (1991). Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association, 86(416), 953–963. https://doi.org/10.2307/2290511

[11] Lalchand, V., & Rasmussen, C. E. (2019). Approximate inference for fully Bayesian Gaussian process regression. Proceedings of Machine Learning Research, 118, 1–12. https://doi.org/10.48550/arXiv.1912.13440