Machine Learning−Enabled Probabilistic Digital Twin for Halftone-Encoded Programmable Mechanical Heterogeneity

Programmable mechanical heterogeneity provides a powerful strategy for tailoring deformation behavior in architected materials. However, establishing predictive relationships between encoded material distributions and mechanical response remains challenging due to complex, nonlinear deformation. Here, we present a machine learning−enabled probabilistic digital twin for halftone-encoded architected materials fabricated via a binary, single-resin additive manufacturing approach. Specimens with systematically varied stiff domain fractions (0−50%) are subjected to uniaxial tensile loading, and deformation morphologies at large strain (60%) are used as input to a convolutional neural network, achieving a classification accuracy of 0.918 ± 0.046. Misclassifications occur primarily between adjacent stiffness states, consistent with the gradual variation in deformation morphology across the mechanical design space. To enable continuous prediction, classification outputs are reformulated through a probabilistic inference framework, where softmax probabilities are interpreted as distributions and converted into continuous estimates via probability-weighted averaging. Validation using four unseen specimens with an intermediate stiffness fraction of 25% provides a proof-of-concept demonstration of prediction at an unseen intermediate state, with estimates remaining within physically meaningful neighboring intervals. This approach establishes deformation morphology as a physically informative descriptor of encoded mechanical heterogeneity, enabling rapid, non-destructive prediction without constitutive modeling or finite element analysis. The framework provides a scalable pathway for integrating additive manufacturing, image-based mechanical testing, and data-driven modeling for the design and evaluation of architected materials.