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The topological simulation of acoustic waves has induced unconventional propagation characteristics, thereby offering extensive application potential in the field of acoustics. In this paper, we propose a machine learning-assisted method for the inverse design of acoustic wave topological edge states and demonstrate its practical applicability. Leveraging the predictions from a trained artificial neural network algorithm, the design of wide-bandwidth topological insulators is achieved, with simulation results indicating an approximately 2.8-fold enlargement of the single-cell topological bandgap. Further investigation into their wide-bandwidth topological transport properties is conducted. Additionally, two distinct functional acoustic routing devices are devised. Superior performance of the wide-bandwidth acoustic topological devices has been verified through simulation experiments. This approach provides an efficient and viable avenue for the design and optimization of acoustic devices, with the potential to enhance the management and control efficiency of acoustic signal propagation. [ABSTRACT FROM AUTHOR]