Complex Geometry

Complex geometry research focuses on developing methods to efficiently model, simulate, and analyze systems with intricate shapes and topologies. Current efforts concentrate on applying and adapting machine learning models, including neural networks (e.g., PINNs, FNOs, transformers), implicit neural representations, and generative models, to solve partial differential equations on complex geometries and optimize designs within manufacturing constraints. This work is crucial for advancing simulations in diverse fields like fluid dynamics, robotics, and medical imaging, enabling faster and more accurate predictions and design optimization in challenging scenarios.