Homogenisation-based topology optimisation for convection-dominated heat transfer incorporated with neural network surrogate modelling

Multi-scale topology optimisation has emerged as a promising design approach for microchannel cooling. However, convection effects have not been adequately addressed in previous works on homogenised thermal modelling. The key challenge lies in the nonlinear dependence of the effective diffusion tensor on both the unit cell parameters and the local flow field, making it computationally infeasible to pre-compute and interpolate the tensor across all possible combinations. This paper introduces a neural network surrogate model to learn this nonlinear operator, enabling real-time prediction of the effective diffusion tensor during optimisation without the need for online homogenisation. The automatic differentiation capability of the neural network is leveraged to compute the gradients required for sensitivity analysis. By integrating the surrogate model into a gradient-based optimisation framework, the cell parameters are optimised at the macro-scale, followed by a straightforward de-homogenisation process to reconstruct the micro-scale pin-fin design. A variety of two-dimensional design examples are presented to demonstrate the validity and effectiveness of the proposed homogenisation-based topology optimisation framework.