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The phase-field method is an attractive computational tool for simulating microstructural evolution during phase separation, including solidification and spinodal decomposition. However, the high computational cost associated with solving phase-field equations currently limits our ability to comprehend phase transformations. This article reports a novel phase-field emulator based on the tensor decomposition of the evolving microstructures and their corresponding two-point correlation functions to predict microstructural evolution at arbitrarily small time scales that are otherwise nontrivial to achieve using traditional phase-field approaches. The reported technique is based on obtaining a low-dimensional representation of the microstructures via tensor decomposition, and subsequently, predicting the microstructure evolution in the low-dimensional space using Gaussian process regression (GPR). Once we obtain the microstructure prediction in the low-dimensional space, we employ a hybrid input–output phase-retrieval algorithm to reconstruct the microstructures. As proof of concept, we present the results on microstructure prediction for spinodal decomposition, although the method itself is agnostic of the material parameters. Results show that we are able to predict microstructure evolution sequences that closely resemble the true microstructures (average normalized mean square of 6.78×10^−7) at time scales half of that employed in obtaining training data. Our data-driven microstructure emulator opens new avenues to predict the microstructural evolution by leveraging phase-field simulations and physical experimentation where the time resolution is often quite large due to limited resources and physical constraints, such as the phase coarsening experiments previously performed in microgravity. 

Abstract Self-assembly by spinodal decomposition is known to be a viable route for synthesizing nanoscaled interfaces in a variety of materials, including metamaterials. In order to tune the response of these specialized materials to external stimuli, knowledge of processing-nanostructure correlations is required. Such an understanding is more challenging to obtain purely by experimental means due to complexity of multicomponent atomic diffusion mechanisms that govern the nanostructural self-assembly. In this work, we introduce a phase-field modeling approach which is capable of simulating the nanostructural evolution in ternary alloy films that are typically synthesized using physical vapor deposition. Based on an extensive parametric study, we analyze the role of the deposition rate and alloy composition on the nanostructural self-assembly in ternary alloy films. The simulated nanostructures are categorized on the basis of nanostructured morphology and mapped over a compositional space to correlate the processing conditions with the film nanostructures. The morphology maps reveal that while deposition rate governs the nanostructural evolution at around equi-molar compositions, the impact of composition on nanostructuring is more pronounced when the atomic ratios of alloying elements are skewed.