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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. 

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.