Machine learning approaches are introduced to model the three-dimensional topside total electron content (TEC) using multiple low Earth orbit (LEO) satellites. The three-dimensional topside TEC can be described by empirical models, such as the NeQuick-G or IRI-2016 model, which has limited accuracy. In this study, we proposed two models based on eXtreme Gradient Boosting (XGBoost) and neural network (NN) to estimate the three-dimensional topside TEC. The models were trained using onboard GNSS observations from 21 LEO satellites at different orbit altitudes, and a genetic algorithm (GA) was applied to optimize the hyperparameters of models. The differential slant total electron content (dSTEC) assessment shows that the XGBoost-GA model outperforms the IRI-2016 and NeQuick-G models, and an accuracy improvement of about 19.5% and 44.8% can be achieved, respectively. Compared to the empirical models, the XGBoost-GA model also achieves an accuracy improvement of about 40% in the LEO-based vertical TEC (VTEC) accuracy. XGBoost-GA and NN-GA also outperform the empirical models in terms of positioning accuracy. With more LEO satellites, ML techniques can be a key processing approach in modeling the topside ionosphere.