Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System
This work addresses the challenge of accurate data-driven simulations in fields like finance or physics, though it is incremental as it builds on existing GAN methods with new regularization techniques.
The authors tackled the problem of probabilistic forecasting for random dynamical systems without distributional assumptions by developing a deep learning model combining a recurrent neural network and a generative adversarial network (GAN), with results validated on three stochastic processes with complex noise structures.
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.