# Uncertainty Quantification in Multivariable Regression for Material Property Prediction with Bayesian Neural Networks

arXiv: https://arxiv.org/abs/2311.02495 · HTML: https://mlsanity.com/paper/2311.02495/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 62 references that are in the map.
- First posted on arXiv 4 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (2020)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [A Variance Maximization Criterion for Active Learning](https://mlsanity.com/paper/1706.07642/) (2017)

## Built on by (most cited first, 5 of 5)

- [Benchmarking GNNs for OOD Materials Property Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2511.11697/) (2025)
- [Gradient Regularized Natural Gradients](https://mlsanity.com/paper/2601.18420/) (2026)
- [Predictive Modeling and Uncertainty Quantification of Fatigue Life in Metal Alloys using Machine Learning](https://mlsanity.com/paper/2501.15057/) (2025)
- [Comparison of Deterministic and Probabilistic Machine Learning Algorithms for Precise Dimensional Control and Uncertainty Quantification in Additive Manufacturing](https://mlsanity.com/paper/2509.16233/) (2025)
- [Machine Learning-based Correlation of Charpy Impact Properties Between Sub-sized and Standard-sized Specimens for Nuclear Structural Materials](https://mlsanity.com/paper/2607.10412/) (2026)

## Abstract (arXiv)

With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including the multi-scale and multi-physics nature of advanced materials, intricate interactions between numerous factors, limited availability of large curated datasets for model training, etc. Recently, Bayesian Neural Networks (BNNs) have emerged as a promising approach for UQ, offering a probabilistic framework for capturing uncertainties within neural networks. In this work, we introduce an approach for UQ within physics-informed BNNs, which integrates knowledge from governing laws in material modeling to guide the models toward physically consistent predictions. To evaluate the effectiveness of this approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of collected measurements from creep tests demonstrates the ability of BNNs to produce accurate point and uncertainty estimates that are competitive or exceed the performance of the conventional method of Gaussian Process Regression. Similarly, we evaluated the suitability of BNNs for UQ in an active learning application and reported competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs. The codes are available at: https://github.com/avakanski/Creep-uncertainty-quantification.