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

arXiv: https://arxiv.org/abs/2512.18104 · HTML: https://mlsanity.com/paper/2512.18104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 64 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Estimating Epistemic and Aleatoric Uncertainty with a Single Model](https://mlsanity.com/paper/2402.03478/) (2024)
- [Calibrated Reliable Regression using Maximum Mean Discrepancy](https://mlsanity.com/paper/2006.10255/) (2020)
- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison](https://mlsanity.com/paper/2103.10522/) (2021)
- [Gaussians on Riemannian Manifolds: Applications for Robot Learning and Adaptive Control](https://mlsanity.com/paper/1909.05946/) (2019)
- [alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction](https://mlsanity.com/paper/2201.08506/) (2022)
- [Clarifying Trust of Materials Property Predictions using Neural Networks with Distribution-Specific Uncertainty Quantification](https://mlsanity.com/paper/2302.02595/) (2023)
- [Bayesian neural networks for predicting uncertainty in full-field material response](https://mlsanity.com/paper/2406.14838/) (2024)
- [Orientation-aware interaction-based deep material network in polycrystalline materials modeling](https://mlsanity.com/paper/2502.02457/) (2025)
- [Probabilistic Neural Networks (PNNs) for Modeling Aleatoric Uncertainty in Scientific Machine Learning](https://mlsanity.com/paper/2402.13945/) (2024)

## Built on by (most cited first, 1 of 1)

- [Deep material network for homogenization of piezoelectric composites](https://mlsanity.com/paper/2606.22566/) (2026)

## Abstract (arXiv)

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.