A Machine Learning-Accelerated Bayesian Framework for Solving Inverse Heat Conduction Problems
Year: 2026
Type: article
Abstract: Inverse heat conduction problems (IHCPs) are fundamental to thermal engineering for estimating unknown boundary conditions, such as surface heat flux, from temperature measurements. Traditional numerical approaches are computationally expensive due to repeated evaluations of physics-based forward solvers within optimization or sampling frameworks. This study introduces an efficient computational framework that combines artificial neural networks (ANNs) with Bayesian inference to accelerate parameter estimation while preserving statistical rigor. A two-dimensional steady-state heat conduction problem is used for demonstration, where an analytical solution generates temperature datasets under varying thermal loads. These data train an ANN surrogate model that approximates the forward heat equation. The surrogate is then embedded within a Markov Chain Monte Carlo (MCMC) method using the Metropolis-Hastings algorithm for Bayesian inference. This approach enables rapid estimation of unknown heat flux values and quantification of uncertainty from noisy temperature data. Results show that the ANN accurately captures the system’s nonlinear behavior, allowing the Bayesian model to converge efficiently to precise posterior distributions with significantly reduced computational cost. This work demonstrates a scalable, data-driven framework for real-time thermal system monitoring and diagnostics.
Authors: Al Hammad, Umaeer, Dutta, Prashanta
Institution: Washington State University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160230957