Machine Learning for Prediction with Missing Dynamics

Understand

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques.

• The proposed framework reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics.
• We demonstrate the effectiveness of the proposed framework with a theoretical guarantee of a path-wise convergence of the resolved variables up to finite time and numerical tests on prototypical models in various scientific domains.
• These include the 57-mode barotropic stress models with multiscale interactions that mimic the blocked and unblocked patterns observed in the atmosphere, the nonlinear Schr\"{o}dinger equation which found many applications in physics such as optics and Bose-Einstein-Condense, the Kuramoto-Sivashinsky equation which spatiotemporal chaotic pattern formation models trapped ion mode in plasma and phase dynamics in reaction-diffusion systems.