Ya Wen presents her M.Sc. thesis on "Surrogate-Based Topology Optimization for Binary Parametric PDE Problems"

Abstract:
Heat conduction topology optimization plays an important role in the design of efficient thermal management structures in engineering fields such as electronic devices, automotive systems, and aerospace applications. Traditional model-driven topology optimization methods typically combine numerical analysis techniques, such as the finite element method (FEM) and the finite volume method (FVM), with gradient-based optimization algorithms such as the method of moving asymptotes (MMA) to obtain high-quality optimized structures. However, these methods require an iterative optimization process with repeated solving the governing heat conduction equation, leading to high computational cost. This issue becomes particularly significant for high-resolution problems, where the required computational time increases
substantially. The objective of this thesis is to propose a deep learning-based model for the rapid prediction of optimal structures in heat conduction topology optimization problems. Unlike existing approaches that primarily focus on accelerating individual optimization iterations, this work aims to directly predict the final optimized material distribution from given thermal boundary conditions and problem parameters, thereby replacing the conventional iterative topology
optimization process. To achieve this objective, a numerical heat conduction topology optimization framework is developed based on the open-source topology optimization software TopOpt. This software uses the finite element method, the SIMP interpolation method, and the MMA optimization algorithm to generate high-quality reference solutions. Based on these numerical results, datasets are constructed to train deep learning–based models for learning the mapping from different thermal boundary conditions to the corresponding optimized topologies. A UNet-based convolutional neural network is employed for image-to-image topology prediction, and a fully connected neural network is used as a baseline model for comparison. The results demonstrate that the UNet-based model can accurately predict optimized structures for heat conduction topology optimization problems. In particular, the UNet-based model significantly outperforms the fully connected network in terms of prediction accuracy and structural fidelity. Moreover, increasing the dataset size substantially improves the generalization capability of the model under varying thermal boundary conditions. Further finite element simulations verify that the predicted structures exhibit thermal performance comparable to that of numerically optimized designs, while achieving a significant reduction in computational cost.