Invariant Torus

Invariant tori are mathematical structures representing periodic or quasi-periodic behavior in dynamical systems, and their identification is crucial for simplifying complex models. Current research focuses on developing efficient algorithms, such as those leveraging machine learning and lattice reduction techniques, to identify and analyze these tori from data, particularly in high-dimensional systems. This work has implications for reduced-order modeling in various fields, including improving the performance of distributed computing systems and enabling privacy-preserving machine learning through homomorphic encryption. Furthermore, understanding invariant tori is essential for characterizing topological properties of data and advancing our understanding of complex phenomena in physics and other scientific domains.