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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 CO₂working capacity and CO₂/N₂selectivity properties.

The atomic structure at the interface between two-dimensional (2D) and three-dimensional (3D) materials influences properties such as contact resistance, photo-response, and high-frequency electrical performance. Moiré engineering is yet to be utilized for tailoring this 2D/3D interface, despite its success in enabling correlated physics at 2D/2D interfaces. Using epitaxially aligned MoS₂/Au{111} as a model system, we demonstrate the use of advanced scanning transmission electron microscopy (STEM) combined with a geometric convolution technique in imaging the crystallographic 32 Å moiré pattern at the 2D/3D interface. This moiré period is often hidden in conventional electron microscopy, where the Au structure is seen in projection. We show, via ab initio electronic structure calculations, that charge density is modulated according to the moiré period, illustrating the potential for (opto-)electronic moiré engineering at the 2D/3D interface. Our work presents a general pathway to directly image periodic modulation at interfaces using this combination of emerging microscopy techniques.