Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins

TL;DR

This paper introduces the Variational Deep Material Network (VDMN), a physics-informed surrogate model that efficiently captures microstructure-induced uncertainties for robust materials digital twins, enabling accurate forward predictions and inverse calibrations.

Contribution

The VDMN uniquely embeds variational distributions within a hierarchical architecture to model aleatoric uncertainties in microstructure-based material behavior.

Findings

Successfully predicts nonlinear mechanical variability in polymer composites.

Quantitatively identifies overlapping sources of uncertainty in material properties.

Demonstrates efficient uncertainty propagation during training and prediction.

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 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.