Reproduce “Data-driven discovery of intrinsic dynamics” on OpenResearch

About this paper

Daniel Floryan, Michael D. Graham

Researchers from the University of Houston and the University of Wisconsin–Madison developed CANDyMan, a data-driven method that integrates manifold theory with neural networks to discover minimal-dimensional dynamical models directly from high-dimensional time series data. This approach represents complex manifolds as collections of overlapping charts, achieving intrinsic dimensionality and providing accurate long-term predictions by overcoming limitations of single-chart dimension reduction techniques.

Key insights

• Decomposing a complex manifold into overlapping charts enables the learning of truly intrinsic-dimensional representations, circumventing the limitations of global parameterization for topologically non-trivial spaces.
• By independently training local autoencoders and dynamics models, the method achieves smooth transitions between charts through implicit transition maps formed by composing local encoders and decoders.
• The modular, localized approach to learning simplifies the problem of modeling complex global dynamics, making it robust to non-uniform data distributions and enabling parallelizable training.

Summary by alphaXiv.