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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月9日

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  • Andreas E. Robertson,
  • Samuel B. Inman,
  • Ashley T. Lenau,
  • Ricardo A. Lebensohn,
  • Dongil Shin,
  • Brad L. Boyce,
  • Rémi Dingreville

摘要

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.