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As modern electronic devices are increasingly miniaturized and integrated, their performance relies more heavily on effective thermal management. In this regard, two-phase cooling methods which capitalize on thin-film evaporation atop structured porous surfaces are emerging as potential solutions. In such porous structures, the optimum heat dissipation capacity relies on two competing objectives that depend on mass and heat transfer. Optimizing these objectives for effective thermal management is challenging due to the simulation costs and the high dimensionality of the design space which is often a voxelated microstructure representation that must also be manufacturable. We address these challenges by developing a data-driven framework for designing optimal porous microstructures for cooling applications. In our framework, we leverage spectral density functions to encode the design space via a handful of interpretable variables and, in turn, efficiently search it. We develop physics-based formulas to simulate the thermofluidic properties and assess the feasibility of candidate designs based on offline image-based analyses. To decrease the reliance on expensive simulations, we generate multi-fidelity data and build emulators to find Pareto-optimal designs. We apply our approach to a canonical problem on evaporator wick design and obtain fin-like topologies in the optimal microstructures which are also characteristics often observed in industrial applications. 

Abstract Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are increasingly used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. Existing multi-fidelity BO (MFBO) methods operate under the following two assumptions: (1) Leveraging global (rather than local) correlation between HF and LF sources, and (2) Associating all the data sources with the same noise process. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. To dispense with these incorrect assumptions, we propose an MF emulation method that (1) learns a noise model for each data source, and (2) enables BO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.