Machine-learning inference of fluid variables from data using reservoir computing
Machine-learning inference of fluid variables from data using reservoir computing
WeÌýinferÌýbothÌýmicroscopicÌýandÌýmacroscopicÌýbehaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference,ÌýweÌýassume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic.ÌýWeÌýpresent two ways of inference of the complex behavior; the first called partial-inference requires continued knowledge of partial time-series data during the inference as well as past time-series data, while the second called full-inference requires only past time-series data as training data. For the first case,ÌýweÌýare able toÌýinferÌýlong-time motion ofÌýmicroscopicÌýfluid variables. For the second case,ÌýweÌýshow that the reservoir dynamics constructed from only past data of energy functions canÌýinferÌýthe future behavior of energy functions and reproduce the energy spectrum. It is also shown thatÌýweÌýcanÌýinferÌýa time-series data from only one measurement by using the delay coordinates. These implies that the obtained two reservoir systems constructed without the knowledge ofÌýmicroscopicÌýdata are equivalent to the dynamical systems describingÌýmacroscopicÌýbehavior of energy functions.