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Abstract Artificial intelligence and machine learning frameworks have become powerful tools for establishing computationally efficient mappings between inputs and outputs in engineering problems. These mappings have enabled optimization and analysis routines, leading to innovative designs, advanced material systems, and optimized manufacturing processes. In such modeling efforts, it is common to encounter multiple information (data) sources, each varying in specifications. Data fusion frameworks offer the capability to integrate these diverse sources into unified models, enhancing predictive accuracy and enabling knowledge transfer. However, challenges arise when these sources are heterogeneous, i.e., they do not share the same input parameter space. Such scenarios occur when domains differentiated by complexity such as fidelity, operating conditions, experimental setup, and scale, require distinct parametrizations. To address this challenge, a two-stage heterogeneous multi-source data fusion framework based on the input mapping calibration (IMC) and the latent variable Gaussian process (LVGP) is proposed. In the first stage, the IMC algorithm transforms the heterogeneous input parameter spaces into a unified reference parameter space. In the second stage, an LVGP-enabled multi-source data fusion model constructs a single-source-aware surrogate model on the unified reference space. The framework is demonstrated and analyzed through three engineering modeling case studies with distinct challenges: cantilever beams with varying design parametrizations, ellipsoidal voids with varying complexities and fidelities, and Ti6Al4V alloys with varying manufacturing modalities. The results demonstrate that the proposed framework achieves higher predictive accuracy compared to both independent single-source and source-unaware data fusion models. 

Abstract 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. 

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.