Manifold Constraint

Manifold constraint research focuses on developing methods to efficiently handle data and processes confined to complex, lower-dimensional spaces (manifolds) embedded within higher-dimensional ambient spaces. Current research emphasizes incorporating manifold constraints into various machine learning algorithms, including generative models (e.g., diffusion models, Riemannian flows), reinforcement learning, and motion planning, often leveraging neural networks, neural ordinary differential equations, and optimization techniques like Riemannian coordinate descent and ADMM. This work is significant because it enables more accurate and efficient modeling of real-world systems with inherent constraints, such as robotic systems, protein dynamics, and various inverse problems, leading to improvements in areas like drug discovery, robotics control, and image processing.