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Melting is a high temperature process that requires extensive sampling of configuration space, thus making melting temperature prediction computationally very expensive and challenging. Over the past few years, I have built two methods to address this challenge, one via direct density functional theory (DFT) molecular dynamics (MD) simulations and the other via deep learning graph neural networks. The DFT approach is based on statistical analysis of small-size solid-liquid coexistence MD simulations. It eliminates the risk of metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Being both accurate and efficient (at the speed of several days per material), it is considered as one of the best methods for direct DFT melting temperature calculation. The deep learning method is based on graph neural networks that effectively handles permutation invariance in chemical formula, which drastically improves efficiency and reduces cost. At the speed of milliseconds per material, the model is extremely fast, while being moderately accurate, especially within the composition space expanded by the dataset. I have implemented both methods into automated computer code packages, making them publicly available and free to download. The DFT and deep learning methods are highly complementary to each other, and hence they can be potentially well integrated into a framework for melting temperature prediction. I demonstrated examples of applying the methods to materials design and discovery of high-melting-point materials.