Modeling Unknown Stochastic Dynamical System via Autoencoder
This work addresses the challenge of modeling complex stochastic systems for applications in fields like physics and engineering, though it appears incremental as it builds on autoencoder methods.
The authors tackled the problem of learning predictive models for unknown stochastic dynamical systems from trajectory data, achieving accurate long-term predictions using short data bursts and handling non-Gaussian noises.
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.