Discretization-optimized Bayesian model calibration for nonlinear constitutive modeling in heat conduction

2026-04-01

AI Summary

This work addresses the challenge of balancing numerical discretization error and model complexity in the inverse identification of temperature-dependent nonlinear thermal conductivity from transient temperature data. A Bayesian calibration framework is proposed that jointly optimizes the parametrization of the thermal conductivity function and the numerical discretization strategy. By integrating gradient-based optimization, adaptive mesh refinement, and an uncertainty-driven stopping criterion grounded in Morozov’s discrepancy principle, the method effectively mitigates overfitting while maintaining high accuracy. Validation on both synthetic and experimental data demonstrates that the approach achieves precise inference of thermal conductivity at low computational cost, aligning numerical and modeling errors with the level of measurement noise and thereby significantly enhancing the robustness and efficiency of nonlinear constitutive relation identification.

Abstract

We present a Bayesian model calibration framework for inferring nonlinear constitutive relationships in heat conduction problems, with a focus on temperature-dependent thermal conductivity. The proposed framework integrates gradient-based optimization and uncertainty quantification (UQ) to address the inverse problem of estimating the conductivity function from transient temperature measurements. A key contribution is an adaptive algorithm that sequentially refines both the numerical discretization for model simulation, and the model complexity used to represent the conductivity curve. The discretization is optimized through the minimization of a loss function, and Morozov's discrepancy principle is used as an uncertainty-motivated stopping criterion. The model complexity is selected using an approach that balances maximizing the likelihood of the data with penalizing excessive model complexity. As a result, the numerical and modeling biases remain of the same order as the uncertainty imposed by the measurement noise, leading to robust and computationally efficient inference. The methodology is demonstrated on both synthetic and experimental data, showing that it enables accurate calibration of nonlinear constitutive models with minimal overfitting and limited computational cost.

Problem

• Bayesian model calibration
• nonlinear constitutive modeling
• thermal conductivity
• inverse problem
• uncertainty quantification

Innovation

• Bayesian calibration
• adaptive discretization
• nonlinear constitutive modeling
• uncertainty quantification
• Morozov discrepancy principle