# Sketch-Guided Topology Optimization with Enhanced Diversity for Innovative Structural Design
## 2 Related Works
### Deep Learning-Enhanced Topology Optimization  
Deep learning (DL) [39] has shown great potential in learning latent features from large datasets, facilitating tasks like new content exploration in latent spaces and prediction in decision-making tasks. In the field of TO, integrating DL methods has emerged as a promising solution to some of the field's tough challenges. Such studies can be broadly categorized into three types: (1) developing black-box TO solver models that replace traditional iterative TO algorithms [27; 40; 41; 42; 43]; (2) fusing DL with traditional algorithms [13; 44; 45; 46]; and (3) using DL models to replace the finite element analysis (FEA) process, thus accelerating the iterations [47; 48; 49]. Among the first type of study, [PERSON] et al. [42] used an encoder-decoder framework based on convolutional neural networks (CNNs) to establish a mapping from boundary conditions and optimization settings to the solutions of traditional TO algorithms. They further integrated conditional generative adversarial networks (cGANs) to improve image resolution of the outputs. [PERSON] et al. [40] proposed a cGAN-based TO solver model, and incorporated multi-physical field simulation results with the load and boundary conditions to improve the quality of the generated designs. [PERSON] et al. [41] replaced cGANs with a diffusion model [50; 51] as the TO solver, and introduced a surrogate model to ensure structural performance and manufacturability. [PERSON] et al. [43] employed a U-Net model [52] as a 3D TO solver. [PERSON] et al. [27] proposed learning low-dimensional latent space from existing TO designs with a convolutional auto-encoder, then generated diverse designs via a sampling strategy based on design of experiment (DOE) in latent space. Another branch of studies focused on fusing DL methods with iterative TO algorithms. [PERSON] et al. [44] encoded the density function of the Solid Isotropic Material with Penalization (SIMP) method using neural networks (NNs), combining the sensitivity analysis through automatic back-propagation of the NNs and independent FEA module. [PERSON] et al. [45] introduced the FEA results of the initial material distributions as conditional input to the neural-encoded density function. Their results showed improved structural performance and higher computing efficiency. [PERSON] et al. [46] embedded TO within a cGAN framework with loss terms of structural compliance and volume constraints to guide the optimization. [PERSON] et al. [13] used reinforcement learning in an iterative fusion pipeline to improve design diversity. A significant challenge in TO is the computational cost associated with the FEA. To address this, [PERSON] and [PERSON] [48] proposed a dual-model artificial neural network for forward computation and sensitivity analysis of the FEA, with discrepancy loss between the predicted and true FEA results. [PERSON] et al. [49] introduced physics-informed neural networks (PINNs) to simulate the forward and sensitivity analysis of the FEA instead. [PERSON] et al. [47] proposed using a structure-mapping neural network to refine coarse-grained TO solutions into fine-grained ones at each iteration, thereby enabling an FEA to be conducted on low-resolution grids. Although DL-based TO solvers beat traditional iterative algorithms in inference efficiency and design diversity, the generated designs mostly fail in satisfying mechanical constraints and manufacturability, making the DL-based solvers invalid as direct solutions to design problems. Using DL-based methods to replace FEA is effective in accelerating iterations while having a small influence on final outputs. One of the obstacles to using data-driven methods is the difficulty in establishing large datasets. Despite current advancements in incorporating DL, traditional iterative TO algorithms continue to play a critical role in ensuring the reliability and quality of the final designs.