Multitask 3D Convolutional Neural Network–Based Multiphysics Design Exploration of Triply Periodic Minimal Surface Bone Scaffolds

Abstract

<title>Abstract</title> Triply periodic minimal surface (TPMS) scaffolds have emerged as promising candidates for bone tissue engineering due to their ability to balance mechanical stiffness, mass transport, and flow-induced shear environments. However, accurate evaluation of these coupled properties typically relies on computationally intensive finite element and computational fluid dynamics simulations, which limits large-scale exploration of the TPMS design space. In this study, we propose a multitask three-dimensional convolutional neural network (3D-CNN) surrogate model for the concurrent prediction of key effective properties of TPMS bone scaffolds, including apparent elastic modulus, intrinsic permeability, effective diffusivity, and a wall shear stress (WSS)–based exposure metric, directly from voxelized scaffold geometries. A dataset of 1,000 unique TPMS designs spanning gyroid, Schwarz-P, and diamond families was generated and labeled using multiphysics simulations, with additional instances obtained through symmetry-preserving transformations. The surrogate model employs a physically informed seven-channel geometric representation and joint learning across tasks to capture shared structure–property relationships. On a held-out test set, the multitask surrogate demonstrated robust predictive performance across all targets, achieving coefficients of determination up to 0.53-0.55 for transport and mechanical properties in challenging intermediate-porosity regimes, while reducing root mean squared error by approximately 40–55% compared to classical analytical models. Relative to single-task CNNs, multitask learning further reduced prediction errors by 7-12%, particularly for transport- and shear-related quantities. Family-wise and representative-design analyses revealed physically consistent topology-dependent trends, with Schwarz-P structures favoring stiffness, gyroid architectures promoting transport performance, and diamond scaffolds offering balanced trade-offs. Pareto-based exploration confirmed that no single topology is universally optimal, underscoring the need for application-specific scaffold selection.