Levenberg-Marquardt Algorithm for Inverse Heat Transfer Problems: Parameters Estimation
Year: 2026
Type: article
Abstract: Inverse heat transfer problems in materials present significant computational challenges, requiring accurate estimation of unknown thermo-physical properties and boundary conditions from limited experimental measurements. Traditional optimization methods often struggle with ill-posed inverse problems, particularly when dealing with dual Neumann boundary conditions. This research applies to the Levenberg-Marquardt algorithm to solve an inverse heat transfer problem in a plane aluminum wall subjected to unknown heat flux on one boundary while the other side remains thermally insulated. The problem considers unsteady one-dimensional heat conduction with both constant and time-varying heat flux conditions. Using the Levenberg-Marquardt optimization technique, we successfully estimated the material's thermal diffusivity and the unknown boundary heat flux from sparse temperature measurements. The method was validated against analytical solutions for various scenarios including constant heat flux, and linearly varying heat flux. Our results demonstrate high accuracy in parameter estimation even with noisy experimental data, showing robust convergence characteristics. However, the algorithm exhibits notable limitations including sensitivity to initial parameter guesses, potential convergence to local minima rather than global optima. Additionally, the method requires careful tuning of hyper-parameters and may face challenges with highly nonlinear or ill-conditioned problems. Despite these constraints, the Levenberg-Marquardt algorithm's ability to handle nonlinear least-squares problems and provide stable convergence makes it valuable for inverse problems. This work establishes a computational framework for estimating thermo-physical parameters in materials processing applications, with future directions including extensions to multidimensional problems, complex geometries, and adaptive strategies to mitigate the identified limitations.
Authors: Ila, Nazifa I., Dutta, Prashanta
Institution: Washington State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160258476