Multi-fidelity Bayesian optimization of covalent organic frameworks for xenon/krypton separations

Our objective is to search a large candidate set of covalent organic frameworks (COFs) for the one with the largest equilibrium adsorptive selectivity for xenon (Xe) over krypton (Kr) at room temperature. To predict the Xe/Kr selectivity of a COF structure, we have access to two molecular simulation techniques: (1) a high-fidelity, binary grand canonical Monte Carlo simulation and (2) a low-fidelity Henry coefficient calculation that (a) approximates the adsorbed phase as dilute and, consequently, (b) incurs a smaller computational runtime than the higher-fidelity simulation. To efficiently search for the COF with the largest high-fidelity Xe/Kr selectivity, we employ a multi-fidelity Bayesian optimization (MFBO) approach. MFBO constitutes a sequential, automated feedback loop of (1) conduct a low- or high-fidelity molecular simulation of Xe/Kr adsorption in a COF, (2) use the simulation data gathered thus far to train a surrogate model that cheaply predicts, with quantified uncertainty, the low- and high-fidelity simulated Xe/Kr selectivity of COFs from their structural/chemical features, then (3) plan the next simulation (i.e., choose the next COF and fidelity) in consideration of balancing exploration, exploitation, and cost. We find that MFBO acquires the optimal COF among the candidate set of 609 structures using only 30 low-fidelity and seven high-fidelity simulations, incurring only 2%, 4% on average, and 20% on average of the computational runtime of a single-[high-]fidelity exhaustive, random, and BO search, respectively.