Data-driven discovery of intrinsic dynamics

Dynamical models underpin our ability to understand and predict the behaviour of natural systems. Whether dynamical are developed from first-principles derivations or observational data, they predicated on choice state variables. The variables is driven by convenience intuition, and, in data-driven cases, observed often chosen be dimensionality these (and consequently models) can arbitrarily large, obscuring underlying system. In truth highly redundant system a much smaller set latent intrinsic this study we combine mathematical theory manifolds with representational capacity neural networks develop method that learns system’s directly time-series as well predictive for their dynamics. What distinguishes its reduce data nonlinear manifold live on. This enabled concepts charts atlases manifolds, whereby represented collection patches sewn together—a necessary representation attain dimensionality. We demonstrate approach several high-dimensional systems low-dimensional behaviour. resulting framework provides lowest possible dimension, capturing essence Learning minimal representations essential modelling prediction science engineering. Floryan Graham propose deep learning able estimate accurate global sewing together multiple local learnt data.