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Abstract Morphogenetic programs coordinate cell signaling and mechanical interactions to shape organs. In systems and synthetic biology, a key challenge is determining optimal cellular interactions for predicting organ shape, size, and function. Physics-based models defining the subcellular force distribution facilitate this, but it is challenging to calibrate parameters in these models from data. To solve this inverse problem, we created a Bayesian optimization framework to determine the optimal cellular force distribution such that the predicted organ shapes match the experimentally observed organ shapes. This integrative framework employs Gaussian Process Regression, a non-parametric kernel-based probabilistic machine learning modeling paradigm, to learn the mapping functions relating to the morphogenetic programs that maintain the final organ shape. We calibrated and tested the method onDrosophilawing imaginal discs to study mechanisms that regulate epithelial processes ranging from development to cancer. The parameter estimation framework successfully infers the underlying changes in core parameters needed to match simulation data with imaging data of wing discs perturbed with collagenase. The computational pipeline identifies distinct parameter sets mimicking wild-type shapes. It enables a global sensitivity analysis to support the regulation of actomyosin contractility and basal ECM stiffness to generate and maintain the curved shape of the wing imaginal disc. The optimization framework, combined with experimental imaging, identified that Piezo, a mechanosensitive ion channel, impacts fold formation by regulating the apical-basal balance of actomyosin contractility and elasticity of ECM. This workflow is extensible toward reverse-engineering morphogenesis across organ systems and for real-time control of complex multicellular systems. 

Sustainability encompasses many wicked problems involving complex interdependencies across social, natural, and engineered systems. We argue holistic multiscale modeling and decision-support frameworks are needed to address multifaceted interdisciplinary aspects of these wicked problems. This review highlights three emerging research areas for artificial intelligence (AI) and machine learning (ML) in molecular-to-systems engineering for sustainability: (1) molecular discovery and materials design, (2) automation and self-driving laboratories, (3) process and systems-of-systems optimization. Recent advances in AI and ML are highlighted in four contemporary application areas in chemical engineering design: (1) equitable energy systems, (2) decarbonizing the power sector, (3) circular economies for critical materials, and (4) next-generation heating and cooling. These examples illustrate how AI and ML enable more sophisticated interdisciplinary multiscale models, faster optimization algorithms, more accurate uncertainty quantification, smarter and faster data collection, and incorporation of diverse stakeholders into decision-making processes, improving the robustness of engineering and policy designs while focusing on the multifaceted goals and constraints in wicked problems. 

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. 

Bayesian hybrid models (BHMs) fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we demonstrate a scalable computational strategy to embed BHMs in an equation-oriented modelling environment. Thus, this paper generalizes stochastic programming, which traditionally focuses on aleatoric uncertainty (as characterized by a probability distribution for uncertainty model parameters) to also consider epistemic uncertainty, i.e., mode-form uncertainty or systematic bias as modelled by the Gaussian process in the BHM. As an illustrative example, we consider ballistic firing using a BHM that includes a simplified glass-box (i.e., equation-oriented) model that neglects air resistance and a Gaussian process model to account for systematic bias (i.e., epistemic or model-form uncertainty) induced from the model simplification. The gravity parameter and the GP hypermeters are inferred from data in a Bayesian framework, yielding a posterior distribution. A novel single-stage stochastic program formulation using the posterior samples and Gaussian quadrature rules is proposed to compute the optimal decisions (e.g., firing angle and velocity) that minimize the expected value of an objective (e.g., distance from a stationary target). PySMO is used to generate expressions for the GP prediction mean and uncertainty in Pyomo, enabling efficient optimization with gradient-based solvers such as Ipopt. A scaling study characterizes the solver time and number of iterations for up to 2,000 samples from the posterior. 

Patterned charged membranes with engendered useful characteristics can offer selective transport of electrolytes. Chemical patterning across the membrane surface via a physical inkjet deposition process requires precise control of the reactive-ink formulation, which enables the introduction of charged functionality to the membrane. This study develops a new dynamic mathematical model for the primary step of the batch reactive-ink formulation considering an ink mixture of copper sulphate and ascorbic acid. Nonlinear least squares parameter estimation is performed to infer three kinetic model parameters by analysing data from nine dynamic experiments simultaneously. Global sensitivity and Fisher information matrix (FIM) analyses reveal only one kinetic parameter is identifiable from time-series pH measurements. The fitted model can capture the overall nonlinear dynamics of the batch reaction and works best for initial Cu2 + concentrations between 30 and 50 mM. Time-series Cu2 + or Cu+ concentration measurements are recommended in future experiments to elucidate the kinetics of reactive-ink formulation. 

Membrane characterization provides essential information for the scale-up, design, and optimization of new separation systems. We recently proposed the diafiltration apparatus for high-throughput analysis (DATA), which enables a 5-times reduction in the time, energy, and the number of experiments necessary to characterize membrane transport properties. This paper applies formal model-based design of experiments (MBDoE) techniques to further analyse and optimize DATA. For example, the eigenvalues and eigenvectors of the Fisher Information Matrix (FIM) show dynamic diafiltration experiments improve parameter identifiability by 3 orders of magnitude compared to traditional filtration experiments. Moreover, continuous retentate conductivity measurements in DATA improve A-, D-, E-, and ME-optimal MBDoE criteria by between 6 % and 32 %. Using these criteria, we identify pressure and initial concentrations conditions that maximize parameter precision and remove correlations. 

The large number of possible structures of metal–organic frameworks (MOFs) and their limitless potential applications have motivated molecular modelers and researchers to develop methods and models to efficiently assess MOF performance. Some of the techniques include large-scale high-throughput molecular simulations and machine learning models. Despite those advances, the number of possible materials and the potential conditions that could be used still pose a formidable challenge for model development requiring large data sets. Therefore, there is a clear need for algorithms that can efficiently explore the spaces while balancing the number of simulations with prediction accuracy. Here, we present how active learning can sequentially select simulation conditions for gas adsorption, ultimately resulting in accurate adsorption predictions with an order of magnitude lower number of simulations. We model adsorption of pure components methane and carbon dioxide in Cu–BTC. We employ Gaussian process regression (GPR) and use the resulting uncertainties in the predictions to guide the next sampling point for molecular simulation. We outline the procedure and demonstrate how this model can emulate adsorption isotherms at 300 K from 10 −6 to 300 bar (methane)/100 bar (carbon dioxide). We also show how this procedure can be used for predicting adsorption on a temperature–pressure phase space for a temperature range of 100 to 300 K, and pressure range of 10 −6 to 300 bar (methane)/100 bar (carbon dioxide).