Data-driven materials design often encounters challenges where systems possess qualitative (categorical) information. Specifically, representing Metal-organic frameworks (MOFs) through different building blocks poses a challenge for designers to incorporate qualitative information into design optimization, and leads to a combinatorial challenge, with large number of MOFs that could be explored. In this work, we integrated Latent Variable Gaussian Process (LVGP) and Multi-Objective Batch-Bayesian Optimization (MOBBO) to identify top-performing MOFs adaptively, autonomously, and efficiently. We showcased that our method (i) requires no specific physical descriptors and only uses building blocks that construct the MOFs for global optimization through qualitative representations, (ii) is application and property independent, and (iii) provides an interpretable model of building blocks with physical justification. By searching only ~1% of the design space, LVGP-MOBBO identified all MOFs on the Pareto front and 97% of the 50 top-performing designs for the CO₂ working capacity and CO₂/N₂ selectivity properties.

Polymer nanodielectrics present a particularly challenging materials design problem for capacitive energy storage applications like polymer film capacitors. High permittivity and breakdown strength are needed to achieve high energy density and loss must be low. Strategies that increase permittivity tend to decrease the breakdown strength and increase loss. We hypothesize that a parameter space exists for fillers of modest aspect ratio functionalized with charge-trapping molecules that results in an increase in permittivity and breakdown strength simultaneously, while limiting increases in loss. In this work, we explore this parameter space, using physics-based, multiscale 3D dielectric property simulations, mixed-variable machine learning and Bayesian optimization to identify the compositions and morphologies which lead to the optimization of these competing properties. We employ first principle-based calculations for interface trap densities which are further used in breakdown strength calculations. For permittivity and loss calculations, we use continuum scale modelling and finite difference solution of Poisson’s equation for steady-state currents. We propose a design framework for optimizing multiple properties by tuning design variables including the microstructure and interface properties. Finally, we employ mixed-variable global sensitivity analysis to understand the complex interplay between four continuous microstructural and two categorical interface choices to extract further physical knowledge on the design of nanodielectrics.

Global Sensitivity Analysis (GSA) is the study of the influence of any given input on the outputs of a model. In the context of engineering design, GSA has been widely used to understand both individual and collective contributions of design variables on the design objectives. So far, global sensitivity studies have often been limited to design spaces with only quantitative (numerical) design variables. However, many engineering systems also contain, if not only, qualitative (categorical) design variables in addition to quantitative design variables. In this paper, we integrate Latent Variable Gaussian Process (LVGP) with Sobol’ analysis to develop the first metamodel-based mixed-variable GSA method. Through numerical case studies, we validate and demonstrate the effectiveness of our proposed method for mixed-variable problems. Furthermore, while the proposed GSA method is general enough to benefit various engineering design applications, we integrate it with multi-objective Bayesian optimization (BO) to create a sensitivity-aware design framework in accelerating the Pareto front design exploration for metal-organic framework (MOF) materials with many-level combinatorial design spaces. Although MOFs are constructed only from qualitative variables that are notoriously difficult to design, our method can utilize sensitivity analysis to navigate the optimization in the many-level large combinatorial design space, greatly expediting the exploration of novel MOF candidates.