# A Computational Sketch-Based Approach Towards Optimal Product Design Solutions
###### Abstract
It also plays a critical role in optimizing material usage, ensuring that components are neither over-engineered nor under-designed, which contributes to weight reduction and cost efficiency. By providing detailed insights into the physical behavior of a product, FEA bridges the gap between theoretical design and practical application, ensuring that the final product is both functional and manufacturable. Its employment throughout the design process ultimately leads to innovative, high-performance products that meet user needs while minimizing risks and resource consumption. Adaptive Mesh Refinement (AMR) is a computational technique that can be applied in simulation-driven product design procedures to enhance the accuracy and efficiency of numerical analysis [7]. In FEA simulations, AMR is used to refine mesh elements in high-stress regions, such as load-bearing components or areas experiencing significant deformation. This ensures precise stress distribution analysis while maintaining computational efficiency. In addition, during the TO, AMR can refine the mesh around evolving boundaries, allowing for smoother and more accurate topology evolution while minimizing computational costs [8]. Hence, by dynamically refining mesh only where needed, AMR provides more detailed simulation results in critical areas while maintaining global computational efficiency. Additionally, AMR facilitates iterative design optimization by allowing designers to refine specific regions of interest without remeshing the entire model, accelerating convergence toward optimal solutions. Its ability to balance accuracy and computational efficiency makes AMR an invaluable service in developing high-performance, structurally optimized, and manufacturable products. Another technology that can be utilized for TO tasks is Generative AI (Artificial Intelligence), especially in engineering and design applications [9]. Traditional topology optimization methods, such as SIMP (Solid Isotropic Material with Penalization) and level-set methods, rely on iterative solvers and FEA as described in the previous paragraphs. However, generative AI provides new approaches that can enhance or even replace these traditional approaches. Generative AI is transforming TO by accelerating the design process, enabling more complex geometries, as well as reducing reliance on simulation-heavy methods. In particular, neural networks (e.g., CNNs, GANs, and Transformers) can learn from existing optimized designs and generate new ones without running full physics-based simulations [10]. Moreover, Physics-Informed AI models can be trained to respect physical laws, such as stress constraints, material properties, and load conditions like PINNs (Physics-Informed Neural Networks) that can predict optimal material distribution under different loading conditions [11]. Another AI model that can be employed in TO tasks is the Reinforcement Learning (RL) for Adaptive Optimization, where RL agents can iteratively modify a structure to maximize performance metrics using Deep Q-Learning [12]. However, these AI approaches require heavy data requirements, where high-quality training data are needed, and also demand large computational resources in order to train AI models for large-scale problems [13]. In addition, it should be mentioned, that the utilization of these kinds of software modules like CAD and CAE requires commercial software packages that come along with a deep learning curve [14]. Hereupon, the present study introduces an easy-to-apply methodology that incorporates these kinds of numerical technologies via an automated and skilled-free approach compared to CAE. Particularly, the introduced methodology computes automatically the optimized design without human intervention and technical skills. The only requirement of the introduced method compose a representative 2D sketch of the part that contains its critical regions, as well as the external loads and the boundary conditions.