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Group contribution (GC) models are powerful, simple, and popular methods for property prediction. However, the most accessible and computationally efficient GC methods, like the Joback and Reid (JR) GC models, often exhibit severe systematic bias. Furthermore, most GC methods do not have uncertainty estimates associated with their predictions. The present work develops a hybrid method for property prediction that integrates GC models with Gaussian process (GP) regression. Predictions from the JR GC method, along with the molecular weight, are used as input features to the GP models, which learn and correct the systematic biases in the GC predictions, resulting in highly accurate property predictions with reliable uncertainty estimates. The method was applied to six properties: normal boiling temperature (Tb), enthalpy of vaporization at Tb (ΔHvap), normal melting temperature (Tm), critical pressure (Pc), critical molar volume (Vc), and critical temperature (Tc). The CRC Handbook of Chemistry and Physics was used as the primary source of experimental data. The final collected experimental data ranged from 485 molecules for ΔHvap to 5640 for Tm. The proposed GCGP method significantly improved property prediction accuracy compared to the GC-only method. The coefficient of determination (R2) values of the testing set predictions are ≥0.85 for five out of six and ≥0.90 for four out of six properties modeled, and compare favorably with other methods in the literature. Tm was used to demonstrate one way the GCGP method can be tuned for even better predictive accuracy. The GCGP method provides reliable uncertainty estimates and computational efficiency for making new predictions. The GCGP method proved robust to variations in GP model architecture and kernel choice. 

Hybrid (i.e., grey-box) models are a powerful and flexible paradigm for predictive science and engineering. Grey-box models use data-driven constructs to incorporate unknown or computationally intractable phenomena into glass-box mechanistic models. The pioneering work of statisticians Kennedy and O’Hagan introduced a new paradigm to quantify epistemic (i.e., model-form) uncertainty. While popular in several engineering disciplines, prior work using Kennedy–O’Hagan hybrid models focuses on prediction with accurate uncertainty estimates. This work demonstrates computational strategies to deploy Bayesian hybrid models for optimization under uncertainty. Specifically, the posterior distributions of Bayesian hybrid models provide a principled uncertainty set for stochastic programming, chance-constrained optimization, or robust optimization. Through two illustrative case studies, we demonstrate the efficacy of hybrid models, composed of a structurally inadequate glass-box model and Gaussian process bias correction term, for decision-making using limited training data. From these case studies, we develop recommended best practices and explore the trade-offs between different hybrid model architectures. 

We review recent advances in software platforms for model-based design (MBD) organized in five overarching themes — from (1) simulation to optimization, (2) commercial to open-source, (3) process-centric to multiscale, (4) mechanistic to data-driven, and (5) deterministic to uncertain — illustrated with several recent examples in membrane system design. We posit MBD provides (chemical) engineers with principled frameworks to tackle global grand challenges such as sustainable energy, clean water, and equitable access to healthcare by integrating knowledge across disciplines. As such, we predict MBD software, which has historically focused on engineered systems, will evolve to interact with models for natural and social systems more holistically. Finally, we emphasize the importance of open-source software development, especially by users who become contributors.