Gaussian mixture models for model improvement

2026-03-16

AI Summary

This study addresses the persistent challenge of significant discrepancies between physics-based simulation models and real-world measurements, which often arise from modeling biases that are non-local and dependent on sensor placement, thereby hindering targeted correction. To overcome this, the authors propose a non-intrusive and interpretable approach that leverages a Gaussian mixture model within a Bayesian framework, combined with the Expectation-Maximization (EM) algorithm, to cluster sensor data and automatically identify physically meaningful parameter groups. This enables the discovery of systematic bias patterns without altering the original model structure, ensuring physically consistent and generalizable model calibration. The method successfully identifies key sources of discrepancy in both numerical experiments and a real-world case study involving thermal conduction in a concrete bridge, effectively guiding precise refinement of the underlying physical model.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even after model calibration due to the model discrepancy, which may result from deliberate modeling decisions, ignorance, or lack of knowledge.mIf the mismatch between simulation and measurements are deemed unacceptable, the model has to be improved. Targeted model improvement is challenging due to a non-local impact of model discrepancies on measurements and the dependence on sensor configurations. Many approaches to model improvement, such as Bayesian calibration with additive mismatch terms, gray-box models, symbolic regression, or stochastic model updating, often lack interpretability, generalizability, physical consistency, or practical applicability. This paper introduces a non-intrusive approach to model discrepancy analysis using mixture models. Instead of directly modifying the model structure, the method maps sensor readings to clusters of physically meaningful parameters, automatically assigning sensor readings to parameter vector clusters. This mapping can reveal systematic discrepancies and model biases, guiding targeted, physics-based refinements by the modeler. The approach is formulated within a Bayesian framework, enabling the identification of parameter clusters and their assignments via the Expectation-Maximization (EM) algorithm. The methodology is demonstrated through numerical experiments, including an illustrative example and a real-world case study of heat transfer in a concrete bridge.

Problem

• model discrepancy
• model improvement
• Gaussian mixture models
• physical systems
• sensor configurations

Innovation

• Gaussian mixture models
• model discrepancy
• non-intrusive modeling
• Bayesian framework
• Expectation-Maximization algorithm