Crystal structure prediction starting from the chemical composition alone has been one of the long-standing challenges in theoretical solid state physics,chemistry,and materials science.While there has been steady progress in predicting the crystal structures of elementary crystals and binary alloys,exploration of complex binary,ternary,and quaternary systems has required more advanced algorithms for configuration space exploration and faster but reliable methods for energy evaluation.In the evaluation of energies of target structures,first-principles calculations are accurate but time-consuming.By contrast,calculations based on classical potentials are fast and applicable to very large systems but are limited in accuracy.We developed an adaptive genetic algorithm (GA) which is an efficient scheme for complex crystal structure prediction.It combines the speed of structure exploration by classical potentials with the accuracy of DFT calculations in an adaptive and iterative way.This strategy increases the efficiency of the DFT-based GA by several orders of magnitude.This gain allows a considerable increase in the size and complexity of systems that can be studied by first principles.Structure prediction in the Mg-Si-O systems is an outstanding example of materials discovery at extreme conditions of planetary interiors where a wealth of novel phases with exotic properties is expected to exist.By using our adaptive genetic algorithm scheme,we predicted several stable structures of the compounds vital for dissociation of MgSiO3,and found a new class of pressure-induced phase transitions of MgSiO3 post-perovskite.