Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System

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.

References in corpus (14)

• GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
• Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation
• Time Series Forecasting With Deep Learning: A Survey
• Deep learning for universal linear embeddings of nonlinear dynamics
• Data-driven discovery of coordinates and governing equations
• How Generative Adversarial Networks and Their Variants Work: An Overview
• Data Driven Governing Equations Approximation Using Deep Neural Networks
• Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters
• Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems
• Deep learning algorithm for data-driven simulation of noisy dynamical system
• Improving Generalization and Stability of Generative Adversarial Networks
• Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows
• Disentangled Recurrent Wasserstein Autoencoder
• Towards a Better Global Loss Landscape of GANs