Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks
This work provides a standardized approach for researchers to test and compare methods in data-driven modeling of dynamical systems, particularly for partially observed systems where exact models are unavailable.
The paper presents an overview and implementation details of the Flow Map Learning (FML) framework, which uses deep neural networks to model unknown dynamical systems from data, and introduces benchmark problems with numerical results to ensure reproducibility.
Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems. A remarkable feature of FML is that it is capable of producing accurate predictive models for partially observed systems, even when their exact mathematical models do not exist. In this paper, we present an overview of the FML framework, along with the important computational details for its successful implementation. We also present a set of well defined benchmark problems for learning unknown dynamical systems. All the numerical details of these problems are presented, along with their FML results, to ensure that the problems are accessible for cross-examination and the results are reproducible.