Abstract

With the development of machine learning techniques and the augment of observational datasets, system reconstruction and prediction have been focal topics in the communities of science and engineering.  Although large datasets are always required for accurate reconstruction and long-term prediction, few time series data of high-dimension or data of poor quality are often available.  Here, to conquer this difficulty, we incorporate the dynamical systems theory with the advanced machine learning techniques, establish a series of frameworks for system reconstruction and prediction using few data but of high-dimension.  We also use several representative examples to illustrate our frameworks, respectively.   Finally, we anticipate the future research direction of machine-learning-driven complex dynamical systems.