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  1. Yamashita, Y. ; Kano, M. (Ed.)
    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. 
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  2. Yamashita, Y. ; Kano, M. (Ed.)
    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. 
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  3. Yamashita, Y. ; Kano, M. (Ed.)
    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. 
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  4. 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). 
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  5. null (Ed.)
    Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian decision-making workflow. First, Bayesian calibration is performed to estimate model parameters. We then use the posterior distribution from Bayesian analysis to compute optimal firing conditions to hit a target via a single-stage stochastic program. The case study demonstrates the ability of Bayesian hybrid models to overcome systematic bias from missing physics with fewer data than the pure machine learning approach. Ultimately, we argue Bayesian hybrid models are an emerging paradigm for data-informed decision-making under parametric and epistemic uncertainty. 
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