Discovery of Slow Variables in a Class Of Multiscale Stochastic Systems Via Neural Networks

Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential provide general framework automatically discover such representations. In this paper, we consider multiscale stochastic systems with local slow-fast time scale separation and propose new method encode in an artificial neural network map that extracts slow representation from system. The architecture consists encoder-decoder pair train supervised manner learn appropriate embedding bottleneck layer. We test on number examples illustrate ability correct representation. Moreover, error measure assess quality demonstrate pruning can pinpoint essential coordinates system build