Highly Efficient Discovery of 3D Mechanical Metamaterials via Monte Carlo Tree Search

Machine learning (ML) has surpassed traditional intuition-driven trial-and-error approaches in metamaterial design by employing efficient inverse pipelines based on structure-property mapping. However, three critical challenges impede the applications of ML when extending the geometry from 2D to 3D: exponentially increasing design space dimensionality, scarce high-quality training data, and excessive computational demands. To address these problems, Monte Carlo Tree Search-Active Learning (MCTS-AL), an active learning framework integrating Monte Carlo Tree Search (MCTS), convolutional neural networks (CNNs), and finite element method (FEM) to efficiently explore high-performance 3D mechanical metamaterials using only 100 initial samples within a vast design space (≈7²⁷ possibilities), is proposed. Demonstrated on triply periodic minimal surface (TPMS) metamaterials for stiffness and strength optimization, MCTS-AL achieves 30% higher stiffness than uniform designs, an enhancement of strength of more than 20% compared with benchmark active learning methods (e.g., Bayesian Optimization, BO), and fewer iterations until convergence. T-distributed Stochastic Neighbor Embedding (T-SNE) clustering confirms that the superior performance stems from a comprehensive understanding of the design space and diverse sampling, with optimized structures forming distinct and various clusters. This work establishes a scalable, data-efficient strategy for high-dimensional mechanical metamaterial design and is expected to be applied in other scenarios demanding optimal solution exploration. © 2025 The Author(s). Advanced Science published by Wiley-VCH GmbH.