Microstructure-based variational deep material networks for robust uncertainty quantification in materials digital twins

Abstract Aleatoric uncertainties – irremovable variability in microstructure morphology, constituent behavior, and processing conditions – pose a major challenge to developing uncertainty-robust digital twins. We introduce the Variational Deep Material Network (VDMN), a physics-informed and microstructure-aware surrogate model that enables efficient and probabilistic forward and inverse predictions of material behavior. The VDMN captures microstructure-induced variability by embedding variational distributions within its hierarchical, mechanistic architecture. Using an analytic propagation scheme based on Taylor-series expansion and automatic differentiation, the VDMN efficiently propagates uncertainty through the network during training and prediction. We demonstrate its capabilities in two digital-twin-driven applications: (1) as an uncertainty-aware materials digital twin, it predicts and experimentally validates the nonlinear mechanical variability in additively manufactured polymer composites; and (2) as an inverse calibration engine, it disentangles and quantitatively identifies overlapping sources of uncertainty in constituent properties. Together, these results establish the VDMN as a foundation for uncertainty-robust materials digital twins.

# Materials of engineering and construction. Mechanics of materials # Computer software

Andreas E. Robertson, Samuel B. Inman, Ashley T. Lenau, et al. (2026). "Microstructure-based variational deep material networks for robust uncertainty quantification in materials digital twins". npj Computational Materials. https://doi.org/10.1038/s41524-026-02054-5