Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System

2021/11/04 by Kyongmin Yeo, Zan Li, Yeo, Kyongmin +3
Computer Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Data Analysis #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Generative Adversarial Networks and Image Synthesis #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Statistics and Probability (physics.data-an)

paper · pdf · doi:10.48550/arxiv.2111.03126

openalex publication_date 2021/11/04 · openalex created_date 2021/11/22 · openalex updated_date 2026/07/28

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.

Citations

• Long Short-Term Memory
• Learning to Forget: Continual Prediction with LSTM
• Improving Generalization and Stability of Generative Adversarial Networks
• Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation
• Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
• Time-series forecasting with deep learning: a survey

Related

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• A New Paradigm for Generative Adversarial Networks based on Randomized Decision Rules