Fig. 1 Evolution and effect of reinforcement learning in materials science. a Historical development stages; b publication articles and citations based on the data from the Web of Science; c applications of reinforcement learning in the field of materials science

Fig. 2 Classification of reinforcement learning

Fig. 3 Commonly used reinforcement learning algorithms. a Q-learning; b deep Q-networks; c actor-critic; d deep deterministic policy gradient [40]

Fig. 4 Important structural parameters of cellular metamaterials optimized by Q-learning. a Flowchart of reinforcement learning Ω; b final Ω values for each episode and the band structure of the initial state; c Ω values at every step during the final episode and the band structure of the final state; d evolution paths during the final episode for four tests with different initial states; e state ratios for the four tests with different initial states [59]

Fig. 5 A novel framework leveraging reinforcement learning to predict porosity in metal laser-powder bed fusion processes. a Agent-environment interaction of the traditional reinforcement learning framework adapted for L-PBF optimization; b average reward per episode received by the agent versus standard deviation; c Q-value associated with each state of the parameter space, to be considered as a processing map, with four micrographs and their corresponding location on the map [61]

Fig. 6 Reinforcement learning for multicomponent alloy compositional design: a Schematic of the proposed reinforcement learning-based alloy design; b component fractions and maximum ΔH proposed by the reinforcement learning agent converge within 4,000 training episodes before synthesis and characterization; c evolution of GP regressor performance over iterations; d GP diagonal plot highlighting; e interactions required to train the reinforcement learning agent with the surrogate; f T-SNE visualization of all experimental compositions containing Ti, Ni, Cu, Hf, and Zr [31]

Fig. 7 Reinforcement learning applied to optimize clinch joint characteristics. a Illustration of the deep reinforcement learning framework used in clinch joint simulations; b total reward at each time step for different random seeds; c overview of the resulting clinch joint and its key quality-related geometric characteristics [69]

Fig. 8 A safe and efficient fast charging strategy for energy storage materials based on reduced-order model (ROM) and soft actor-critic (SAC). a Flowchart of fast charging strategy based on SAC; b reward value during training episodes; c maximum terminal voltage; d maximum core temperature; e minimum side reaction; f training performance comparison graph of SAC and other deep reinforcement learning (DRL) Algorithms [76]

Fig. 9 Exploration of nanocluster potential energy surfaces using actor-critic-based DRL. a Schematic of the actor-critic DRL framework; b evolution of episodic rewards during training; c K-means clustering analysis of unique minimum energy configurations identified during training; d, e Energy profiles from early training episodes; f, g, h, i Distribution metrics of Cu nanoclusters during pre- and post-policy learning across twenty episodes [74]

Fig. 10 Coupling of an analytical rolling model and reinforcement learning to design a pass schedule. a Schematic structure of the DDPG algorithm; b evolution of the reward constituents after each iteration; c comparison between the measurements and FRM-predicted values [40]

Fig. 11 Accelerating thermal deformation of titanium aluminide TNM-B1 via reinforcement learning. a Schematic of the reinforcement learning and finite element co-simulation framework using the DDPG reinforcement learning algorithm; b action profiles for the bone compression simulation; c reward profiles for the bone compression simulation; d stress profiles of elements in the bone compression simulation [86]

Fig. 12 The processes and results of the activation and methanation using the reinforcement learning Monte Carlo Tree Search Algorithm. a Framework diagram of the reinforcement learning method-policy gradient (MCTS-PG); b, c test results and datasets of MCTS-PG and the original MCTS; d the search and screening workflow of MCTS-PG [41]

Fig. 13 Summary diagram of reinforcement learning in materials science