Polytopic Autoencoders

Polytopic autoencoders are neural network architectures designed to create low-dimensional representations of complex systems, particularly focusing on representing data within a defined polytope (a geometric shape defined by multiple vertices). Current research emphasizes developing efficient architectures, often incorporating smooth clustering techniques to improve the accuracy and interpretability of the low-dimensional models, and comparing their performance against established methods like Proper Orthogonal Decomposition (POD). This approach holds significant promise for simplifying the control and analysis of high-dimensional systems, such as those described by nonlinear partial differential equations, leading to more efficient computational methods for applications in fluid dynamics and other fields.