Generative artificial intelligence is transforming multiple scientific fields. However, in engineering design applications, such as generating component geometries from desired outcomes, significant challenges remain before reaching practical, functional tools. For instance, Engineering design must comply with multiple physical constraints, like continuity of the solution, conservation of mass and energy, stress convexity with respect to dimensions… When disposing of a direct problem surrogate, countless scenarios must often be evaluated in brute-force optimization to solve inverse problems, resulting in high computational and time costs. Identifying the optimal inputs for a known desired outcome is referred to as the inverse problem [1]. Inverse problems are known to be intractable, ill-posed [2], and frequently falls into the category of Cauchy problems. Consequently, training a surrogate to predict the solution of an inverse problem is often impractical. Moreover, this approach often lacks a mechanism to enforce the problem’s physical constraints. This minisymposium aims to showcase recent advances in optimal generative design and foster collaboration within the scientific community. Topics include, but are not limited to: optimal geometrical design generation, constrained inverse-problem solution methods, artificial intelligence approaches to inverse problems, reinforcement-learning-based inverse-problem solutions, generative adversarial networks and autoencoder generation methodologies. [1] D. Di Lorenzo, V. Champaney, C. Ghnatios, E. Cueto, and F. Chinesta. Physics-informed and graph neural networks for enhanced inverse analysis. Engineering Computation, Nov. 2024. https://doi.org/10.1108/EC-12-2023-0958. [2] P. Jayaraman, J. Desman, M. Sabounchi, G. N. Nadkarni, and A. Sakhuja. A primer on reinforcement learning in medicine for clinicians. NPJ Digit. Med., 7(1):337, Nov. 2024.