Microtubules (MTs), a cellular structure element, exhibit dynamic instability and can switch stochastically from growth to shortening; but the factors that trigger these processes at the molecular level are not understood. We developed a 3D Microtubule Assembly and Disassembly DYnamics (MADDY) model, based upon a bead-per-monomer representation of the alpha beta-tubulin dimers forming an MT lattice, stabilized by the lateral and longitudinal interactions between tubulin subunits. The model was parameterized against the experimental rates of MT growth and shortening, and pushing forces on the Dam1 protein complex due to protofilaments splaying out. Using the MADDY model, we carried out GPU-accelerated Langevin simulations to access dynamic instability behavior. By applying Machine Learning techniques, we identified the MT characteristics that distinguish simultaneously all four kinetic states: growth, catastrophe, shortening, and rescue. At the cellular 25 mu M tubulin concentration, the most important quantities are the MT length L, average longitudinal curvature kappa(long), MT tip width w, total energy of longitudinal interactions in MT lattice U-long, and the energies of longitudinal and lateral interactions required to complete MT to full cylinder U-long(add) and U-lat(add) . At high 250 mu M tubulin concentration, the most important characteristics are L, kappa(long), number of hydrolyzed alpha beta-tubulin dimers n(hyd) and number of lateral interactions per helical pitch n(lat) in MT lattice, energy of lateral interactions in MT lattice U-lat, and energy of longitudinal interactions in MT tip u(long). These results allow greater insights into what brings about kinetic state stability and the transitions between states involved in MT dynamic instability behavior.