Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System

TL;DR

This paper introduces a deep learning framework combining RNNs and GANs, with a novel regularization strategy, to accurately simulate and sample from complex random dynamical systems without assuming specific distributions.

Contribution

It develops a regularization method for GANs using consistency conditions and MMD, enhancing probabilistic forecasting of complex stochastic processes.

Findings

Successfully models complex noise structures in stochastic processes

Regularization improves the stability and accuracy of GAN training

Demonstrates effectiveness on three different stochastic systems

Abstract

We present a deep learning model for data-driven simulations of random dynamical systems without a distributional assumption. The deep learning model consists of a recurrent neural network, which aims to learn the time marching structure, and a generative adversarial network (GAN) to learn and sample from the probability distribution of the random dynamical system. Although GANs provide a powerful tool to model a complex probability distribution, the training often fails without a proper regularization. Here, we propose a regularization strategy for a GAN based on consistency conditions for the sequential inference problems. First, the maximum mean discrepancy (MMD) is used to enforce the consistency between conditional and marginal distributions of a stochastic process. Then, the marginal distributions of the multiple-step predictions are regularized by using MMD or from multiple discriminators. The behavior of the proposed model is studied by using three stochastic processes with complex noise structures.