[Paper Review] Uncertainty Quantification in Multivariable Regression for Material Property Prediction with Bayesian Neural Networks

Longze Li, Jiang Chang+4 more|arXiv (Cornell University)|Nov 4, 2023

Machine Learning in Materials Science54 references4 citations

TL;DR

This paper proposes a physics-informed Bayesian neural network (BNN) framework for uncertainty quantification (UQ) in multivariable regression of material properties, specifically creep rupture life in steel alloys. By integrating physical laws into BNNs via Markov Chain Monte Carlo (MCMC) posterior approximation, the method achieves more reliable uncertainty estimates than variational inference or Gaussian process regression, with experimental validation on three creep test datasets showing competitive or superior performance.

ABSTRACT

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.

Motivation & Objective

• To address the challenge of reliable uncertainty quantification (UQ) in material property prediction due to limited data and complex multi-scale interactions.
• To integrate physical laws from material modeling into Bayesian neural networks for improved predictive consistency and reliability.
• To evaluate the performance of different BNN inference methods—specifically MCMC versus variational inference—for UQ in multivariable regression tasks.
• To demonstrate the framework's effectiveness in active learning and real-world creep rupture life prediction using experimental datasets.

Proposed method

• The framework employs Bayesian Neural Networks (BNNs) to model both predictive mean and uncertainty, using a probabilistic weight distribution over network parameters.
• Physical constraints from governing laws in material science are embedded into the BNN architecture to ensure predictions remain physically consistent.
• Two inference strategies are compared: Markov Chain Monte Carlo (MCMC) for accurate posterior approximation and variational inference for faster, approximate inference.
• The model is trained on three experimental creep test datasets for steel alloys, with uncertainty estimates evaluated against ground-truth measurements.
• The method uses probabilistic outputs to generate predictive distributions, enabling both point estimates and credible intervals for uncertainty quantification.
• Active learning is applied using uncertainty estimates to guide data acquisition, demonstrating the utility of the framework in data-scarce scenarios.

Experimental results

Research questions

• RQ1 Can physics-informed Bayesian neural networks provide more reliable uncertainty estimates for multivariable material property prediction than conventional methods?
• RQ2 How does MCMC-based posterior approximation in BNNs compare to variational inference in terms of predictive accuracy and uncertainty calibration for material property data?
• RQ3 To what extent can incorporating physical laws into BNNs improve the consistency and reliability of predictions in data-limited material science applications?
• RQ4 Can the proposed BNN framework effectively support active learning by identifying informative data points through uncertainty estimation?

Key findings

• The MCMC-based BNN framework produced more reliable uncertainty estimates than variational inference-based BNNs or standard neural networks with probabilistic outputs.
• On three independent creep test datasets, the MCMC-BNN achieved predictive performance competitive with or exceeding that of Gaussian Process Regression, a benchmark method for UQ.
• The integration of physical laws into the BNN architecture significantly improved prediction consistency and reduced physically implausible outputs.
• In active learning applications, uncertainty estimates from the MCMC-BNN effectively guided data selection, demonstrating utility in data-efficient model training.
• The BNN with MCMC inference showed superior calibration of uncertainty intervals, with prediction intervals covering a higher proportion of true values compared to alternative methods.
• The framework's code is publicly available, enabling reproducibility and extension to other material property prediction tasks.