Park, J.; Smith, C.; Tseng, S. Y.; Guidera, J.; Semenov, A. V.; Smirnov, S.; Frank, L. M.; Pao, G. M.

Complex systems such as brains and other interacting biological and physical processes are difficult to represent because they evolve across many variables, scales, and nonlinear interactions. To capture these multivariate, multiscale interactions we have developed Generative Manifold Networks (GMNs) a machine learning framework consisting of a network of linked dynamical systems. The network is discovered by an interaction function which can focus on causality, shared information, nonlinearity or other metric. Network nodes are low--dimensional data--driven state--space manifolds with generator functions accommodating multiscale dynamics. In contrast to many machine learning approaches GMNs have no latent or randomly initialized variables providing transparent explainability. GMNs generate short term dynamics of chaos on par with echo state networks while outperforming them in long term generation of chaos and neural dynamics, but with a markedly reduced number of dimensions and without sensitive dependence on reservoir parameters or random states. As a result of their holistic, multiscale representation GMNs can learn the complete dynamics of a complex system. We further show that GMNs are universal approximators. GMNs are demonstrated on chaotic dynamics, neural and behavioral recordings of the fruit fly and domestic rat with comparisons to echo state networks and crossformer - a time series transformer.