Machine-learning-enabled computational–experimental framework for structure–property mapping in TPMS lattice structures

Abstract Triply periodic minimal surface (TPMS) lattice structures present significant potential for lightweight mechanical systems; however, property-driven design is constrained by the computational expense of repeated finite-element (FE) simulations and the substantial experimental effort required to establish reliable structure–property relationships. This study introduces a computationally efficient and interpretable framework for predicting Young’s modulus and specific stiffness in TPMS lattice structures, integrating surrogate modeling, inverse design, SHAP (Shapley Additive Explanations)-based interpretation, and Bayesian optimization (BO) to efficiently identify high-performing designs, with experimental validation through additive manufacturing and mechanical testing. Seven machine learning models were evaluated on a dataset of 270 FE-simulated TPMS lattices spanning five topological families. The Stacked Ensemble (SE), combining Random Forest, Gradient Boosting, Gaussian Process Regression (GPR), and Deep Neural Network predictors via a Ridge regression meta-learner, achieved the highest predictive accuracy (R² = 0.995 for Young’s modulus; R² = 0.997 for specific stiffness), while GPR demonstrated comparable performance. Both models generalized effectively to unseen designs with errors below 3% and were applied to inverse design, SHAP-based geometry–property interpretation, and Bayesian optimization. The framework identified target-satisfying geometries with errors below 1.1% and explored a design space of 4.47 × 10⁸ configurations in under three hours. Experimental validation confirmed Young’s modulus predictions within 3–16%, while specific stiffness deviations between 37 and 72% were attributed to fabrication-induced density increases rather than surrogate model limitations. The proposed framework offers a scalable, interpretable, robust, and experimentally validated pathway for rapid, property-driven TPMS lattice design.