Modeling Unknown Stochastic Dynamical System via Autoencoder
Zhongshu Xu Yuan Chen Qifan Chen Dongbin Xiu
We present a numerical method to learn an accurate predictive model for an
unknown stochastic dynamical system from its trajectory data. The method seeks
to approximate the unknown flow map of the underlying system. It employs the
idea of autoencoder to identify the unobserved latent random variables. In our
approach, we design an encoding function to discover the latent variables,
which are modeled as unit Gaussian, and a decoding function to reconstruct the
future states of the system. Both the encoder and decoder are expressed as deep
neural networks (DNNs). Once the DNNs are trained by the trajectory data, the
decoder serves as a predictive model for the unknown stochastic system. Through
an extensive set of numerical examples, we demonstrate that the method is able
to produce long-term system predictions by using short bursts of trajectory
data. It is also applicable to systems driven by non-Gaussian noises.