High-dimensional inverse design enables multiple synthesis routes to prescribed carbon nanotube array descriptors

Abstract

Abstract Prescribed synthesis of carbon nanotube (CNT) arrays remains challenging because multiple processing stages jointly regulate array height (H), density (ρ), and orientational order (HOF), creating a nonlinear and non-unique relationship between structural targets and synthesis conditions. Here, we develop an Multilayer perceptron–Differential dvolution (MLP–DE) inverse design framework that searches for an eight-dimensional process space for multiple separated recipes rather than a single optimum. The framework was established from 200 unique water-assisted CVD recipes and evaluated across three prescribed H–ρ–HOF targets. Of 27 independent validation batches, 26 achieved descriptor matching scores above 95%. Importantly, recipes that reached similar array-level states retained variations in CNT diameters and wall structures, showing that comparable macroscopic outcomes can arise from different nanoscale structural realizations. These results challenge the conventional assumption that a prescribed CNT-array state must be approached through progressive refinement around a single local process window. Instead, the same target state can be accessed from multiple separate regions of process space. This descriptor-level route degeneracy reframes inverse synthesis from locating one optimum to resolving multiple experimentally accessible solutions, providing greater design freedom for the controlled synthesis of complex nanomaterials.