Data-Driven Design and Optimization of TPMS Structures: A Critical Review of Deep Learning, Inverse Design, and Multiscale Engineering Applications

Abstract Triply periodic minimal surface (TPMS) structures provide a compact geometric platform for tailoring mechanical, thermal−hydraulic, transport, and energy absorption behaviors, but their coupled design space makes repeated numerical evaluation expensive, particularly for functionally graded and multiscale structures. Data-driven methods have therefore been increasingly used to approximate structure−property relationships and accelerate design exploration. This review critically examines how machine learning and deep learning are being used for TPMS design, with an emphasis on forward property prediction, inverse and generative design, surrogate-assisted optimization, and multiscale topology optimization. Studies from a documented search were classified by the role, demonstrated architecture, and reported validation level. Rather than treating model accuracy as the primary measure of progress, the review compares the reported approaches in terms of training-data requirements, extrapolation behavior, computational savings, design variables, physical constraints, manufacturability, and validation against high-fidelity simulation or experiment, and it separates results obtained on TPMS structures from methods transferred from strut, shell, spinodoid, and other architectures. Most TPMS models are tested on random splits within the sampled design space; few test extrapolation, and where this has been done, failure-related quantities degraded more than elastic properties. In the examples examined, the largest reported gains coincide with functionally graded designs and expanded spatial design freedom, but no study separates the contributions of geometry, search algorithm, and learning model under controlled conditions. Common limitations are the lack of shared benchmark problems, inconsistent simulation and homogenization assumptions, limited treatment of manufacturing variability, uncalibrated uncertainty estimates, and insufficient comparison with classical optimization under equivalent computational budgets. The review therefore positions data-driven methods as acceleration and design-exploration tools rather than replacements for physics-based analysis and established optimization methods, and it proposes a design workflow with explicit rules for accepting a prediction, requesting a high-fidelity evaluation, and accounting for manufacturing deviations.