Embedded Model Bias Quantification with Measurement Noise for Bayesian Model Calibration

2024-10-15

arXiv.org

AI Summary

To address prediction inaccuracy in Bayesian model calibration caused by neglecting model-form uncertainty, this paper proposes an embedded bias quantification framework that jointly infers physical parameters and model bias within Bayesian inference while explicitly coupling measurement noise modeling. The method introduces an interpretable embedded bias structure, designs two noise-robust likelihood functions—significantly enhancing robustness against noisy and outlier-contaminated data—and systematically characterizes the propagation mechanism of bias uncertainty to quantities of interest (QoIs). Evaluated on a transient thermal simulation inverse problem, the framework successfully quantifies bias and propagates uncertainty in heat flux predictions from temperature observations. Results demonstrate markedly improved accuracy in predictive confidence assessment, validating the approach’s dual advantages in reliability and robustness.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

The use of computer simulations to model physical systems has gained significant traction in recent years. A key factor in ensuring the accuracy of these models is the proper calibration of model parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian methods provide a robust framework for quantifying and propagating these uncertainties to model predictions. However, predictions can become inaccurate if model errors are neglected. A promising approach to address this issue involves embedding a bias term in the inference parameters, allowing the quantified bias to influence non-observed Quantities of Interest (QoIs). This paper introduces a more interpretable framework for bias embedding compared to existing methods. Current likelihood formulations that incorporate embedded bias often fail when measurement noise is present. To overcome these limitations, we adapt the existing likelihood models to properly account for noise and propose two new formulations designed to address the shortcomings of the previous approaches. Moreover, we evaluate the performance of this bias-embedding approach in the presence of discrepancies between measurements and model predictions, including noise and outliers. Particular attention is given to how the uncertainty associated with the bias term propagates to the QoIs, enabling a more comprehensive statistical analysis of prediction reliability. Finally, the proposed embedded bias model is applied to estimate the uncertainty in the predicted heat flux from a transient thermal simulation, using temperature observations to illustrate its effectiveness.

Problem

• Quantify model form uncertainty in Bayesian calibration with noise
• Improve interpretability of embedded model inadequacy term
• Propagate uncertainty to unobserved Quantities of Interest reliably

Innovation

• Embed model inadequacy term in inference parameters
• Adapt likelihood models for measurement noise
• Propagate model inadequacy uncertainty to QoIs