Discovery of Slow Variables in a Class Of Multiscale Stochastic Systems Via Neural Networks
Abstract
Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional “heart” remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential to provide a general framework to automatically discover such representations. In this paper, we consider multiscale stochastic systems with local slow-fast timescale separation and propose a new method to encode in an artificial neural network a map that extracts the slow representation from the system. The architecture of the network consists of an encoder–decoder pair that we train in a supervised manner to learn the appropriate low-dimensional embedding in the bottleneck layer. We test the method on a number of examples that illustrate the ability to discover a correct slow representation. Moreover, we provide an error measure to assess the quality of the embedding and demonstrate that pruning the network can pinpoint essential coordinates of the system to build the slow representation.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- May 26, 2022
- Source ID
- 10.1007/s00332-022-09808-7
Entities
People
- Jan S. Hesthaven
- Przemysław Zieliński
Organizations
- Air Force Office of Scientific Research