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Defect dynamics in materials are of central importance to a broad range oftechnologies from catalysis to energy storage systems to microelectronics.Material functionality depends strongly on the nature and organization ofdefects, their arrangements often involve intermediate or transient states thatpresent a high barrier for transformation. The lack of knowledge of theseintermediate states and the presence of this energy barrier presents a seriouschallenge for inverse defect design, especially for gradient-based approaches.Here, we present a reinforcement learning (Monte Carlo Tree Search) based ondelayed rewards that allow for efficient search of the defect configurationalspace and allows us to identify optimal defect arrangements in low dimensionalmaterials. Using a representative case of 2D MoS2, we demonstrate that the useof delayed rewards allows us to efficiently sample the defect configurationalspace and overcome the energy barrier for a wide range of defect concentrations(from 1.5% to 8% S vacancies), the system evolves from an initial randomlydistributed S vacancies to one with extended S line defects consistent withprevious experimental studies. Detailed analysis in the feature space allows usto identify the optimal pathways for this defect transformation andarrangement. Comparison with other global optimization schemes like geneticalgorithms suggests that the MCTS with delayed rewards takes fewer evaluationsand arrives at a better quality of the solution. The implications of thevarious sampled defect configurations on the 2H to 1T phase transitions in MoS2are discussed. Overall, we introduce a Reinforcement Learning (RL) strategyemploying delayed rewards that can accelerate the inverse design of defects inmaterials for achieving targeted functionality.

Learning with Delayed Rewards -- A case study on inverse defect design in 2D materials