Adaptive Finite Difference Mesh Refinement for Transient Heat Transfer in Complex Geometries with Anisotropic Thermal Conductivity using Bayesian Optimization and Machine Learning Surrogate Models

**Abstract:** This research introduces a novel adaptive finite difference method (FDM) for simulating transient heat transfer in complex geometries exhibiting anisotropic thermal conductivity. The approach intelligently refines the computational mesh based on a real-time error estimation technique leveraging Bayesian Optimization (BO) and Machine Learning (ML) surrogate models to predict localized regions demanding higher resolution. This guarantees accurate solutions while minimizing computational cost, offering an immediate advantage over traditional fixed-mesh or coarse adaptive methods. The commercial viability stems from facilitating faster design iterations in thermal management applications across diverse industries including electronics cooling, aerospace heat shields, and microfluidic devices. --- *This document is a part of the Freederia Research Archive. Explore our complete collection of advanced research at [en.freederia.com](https://en.freederia.com), or visit our main portal at [freederia.com](https://freederia.com) to learn more about our mission and other initiatives.*