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Description
Two-dimensional (2D) ultracoherent nanomechanical resonators are promising platforms for room-temperature quantum sensing, precision metrology, and cavity optomechanics, but their performance is often limited by mechanical dissipation, large effective motional mass, and insufficient optomechanical coupling. In this work, we demonstrate that highly symmetric 2D nanomechanical resonators can achieve high quality factors by exploiting localized modes beyond the conventional phononic band-gap mechanism in highly stressed silicon nitride membranes. We develop a hybrid inverse-design strategy that combines Bayesian optimization with topology optimization to efficiently search complex geometries and identify structures with favorable modal properties. In particular, this hybrid strategy is used to maximize the dissipation dilution factor while simultaneously reducing the effective motional mass, two key parameters for high-performance resonator design. Our results show that highly symmetric structures can reach performance metrics comparable to those of band-gap-based phononic crystal resonators, while offering an alternative route for engineering ultracoherent mechanical modes. These findings highlight the potential of highly symmetric membrane architectures for the realization of low-loss, low-mass, and optomechanically favorable resonators for future sensing and quantum technologies.