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Cellular materials have been widely used in load carrying lightweight structures. Although lightweight increases natural frequency, low stiffness of cellular structures reduces natural frequency. Designing structures with higher natural frequency can usually avoid resonance. In addition, because of the less amount of materials used in cellular structures, the energy absorption capability usually decreases such as under impact loading. Therefore, designing cellular structures with higher natural frequency and higher energy absorption capability is highly desired. In this study, machine learning and novel inverse design techniques enable to search a huge space of unexplored structural designs. In this study, machine learning regression and Generative Neural Networks (GANs) were used to form an inverse design framework. Optimal cellular unit cells that surpass the performance of biomimetic structures inspired from honeycomb, plant stems and trabecular bone in terms of natural frequency and impact resistance were discovered using machine learning. The discovered optimal cellular unit cells exhibited 30–100% higher natural frequency and 300% higher energy absorption than those of the biomimetic counterparts. The discovered optimal unit cells were validated through experimental and simulation comparisons. The machine learning framework in this study would help in designing load carrying engineering structures with increased natural frequency and enhanced energy absorption capability.