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Abstract Topological magnons give rise to possibilities for engineering novel spintronics devices with critical applications in quantum information and computation, due to their symmetry-protected robustness and low dissipation. However, to make reliable and systematic predictions about the material realization of topological magnons has been a major challenge, due to the lack of neutron scattering data for most materials and the absence of reliable ab initio calculations for magnons. In this work, we significantly advance the symmetry-based approach for identifying topological magnons through developing a fully automated algorithm, utilizing the theory of symmetry indicators, that enables a highly efficient and large-scale search for candidate materials hosting perturbation-driven topological magnons. This progress not only streamlines the discovery process but also expands the scope of materials exploration beyond previous manual or traditional approaches, offering a powerful tool for uncovering novel topological phases in magnetic systems. Performing a large-scale search over all 1649 magnetic materials in the Bilbao Crystallographic Server (BCS) with a commensurate magnetic order, we discover 387 perturbation-induced topological magnon materials, significantly expanding the pool of topological magnon materials and showing that more than 23% of all commensurate magnetic compounds in the BCS database are topological. We further discuss examples and experimental accessibility of the candidate materials, shedding light on future experimental realizations of topological magnons in magnetic materials. We provide anopen-source programthat checks the symmetry-enforced magnon band topology of any commensurate magnetic structure upon perturbations and allows researchers to reproduce our results.