Flow Map Learning (FML) is a powerful methodology to create data driven predictive models for dynamical systems. This page contains its brief introduction and detailed descriptions of a set of benchmark problems. The content of this page will be updated on a continuous basis.
Some references for FML:
Fully observed system: Qin, Wu, Xiu, Data driven governing equations approximation using deep neural networks, J. Comput. Phys. 2019
Partially observed system: Fu, Chang, Xiu, Learning reduced systems via deep neural networks with memory. JMLMC, 2020.
Non-autonomous system: Qin, Chen, Jakeman, Xiu, Data driven learning of nonautonomous systems, SIAM J. Sci. Comput., 2021.
A review of the technical details and several benchmark problems can be found here:
Churchill, Xiu, Flow Map Learning for unknown dynamical systems: overview, implementation, and benchmarks. (PDF on arXiv)
All files for replicate the example problems in the paper are available for download as a set, or individually below.