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

Abstract

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.