OPTIMIZATION ON 3D DOMAINS WITH IMPLICITLY DEFINED TRIMMING SURFACES SYSTEM IN AI

This paper presents an optimization framework for 3D domains with implicitly defined trimming surfaces system, utilizing artificial intelligence (AI) techniques. Implicitly defined trimming surfaces are widely used in computer-aided design and manufacturing (CAD/CAM) to represent complex geometries. However, optimizing functions defined on these domains poses significant challenges due to their nonlinear and non-convex nature. we propose a novel approach that combines AI algorithms with implicit surface representations to efficiently optimize functions on 3D domains. Our method leverages the power of deep learning models to approximate the implicit surfaces and utilizes advanced optimization algorithms to search for optimal solutions. The contribution of our work lies in the integration of AI techniques into the optimization process. We employ deep neural networks to learn the implicit representation of the trimming surfaces, enabling efficient evaluation of functions on the domain. Additionally, we leverage reinforcement learning algorithms to guide the optimization process, effectively exploring the solution space and discovering optimal solutions. We demonstrate the effectiveness of our approach through several experiments on different 3D domains with implicitly defined trimming surfaces. Our results show that the proposed framework outperforms traditional optimization methods in terms of solution quality and convergence speed. Furthermore, we highlight the flexibility of our approach by showcasing its applicability to various optimization problems, such as shape optimization, structural optimization, and parameter tuning. this research introduces a novel optimization framework that combines AI techniques and implicitly defined trimming surfaces in 3D domains. By leveraging deep learning and reinforcement learning algorithms, we achieve efficient and effective optimization of functions on these complex surfaces. Our approach has the potential to revolutionize the field of CAD/CAM by providing advanced optimization capabilities for designers and engineers working with implicitly defined geometries.