# Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System

arXiv: https://arxiv.org/abs/2111.03126 · HTML: https://mlsanity.com/paper/2111.03126/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 57 references that are in the map.
- First posted on arXiv 4 Nov 2021.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Consistency Regularization for Generative Adversarial Networks](https://mlsanity.com/paper/1910.12027/) (2019)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Stabilizing Training of Generative Adversarial Networks through Regularization](https://mlsanity.com/paper/1705.09367/) (2017)
- [Data Driven Governing Equations Approximation Using Deep Neural Networks](https://mlsanity.com/paper/1811.05537/) (2018)
- [Gradient descent GAN optimization is locally stable](https://mlsanity.com/paper/1706.04156/) (2017)
- [Accelerating Science with Generative Adversarial Networks: An Application to 3D Particle Showers in Multi-Layer Calorimeters](https://mlsanity.com/paper/1705.02355/) (2017)
- [Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Step](https://mlsanity.com/paper/1710.08446/) (2017)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Disentangled Recurrent Wasserstein Autoencoder](https://mlsanity.com/paper/2101.07496/) (2021)
- [Towards a Better Global Loss Landscape of GANs](https://mlsanity.com/paper/2011.04926/) (2020)
- [Deep learning algorithm for data-driven simulation of noisy dynamical system](https://mlsanity.com/paper/1802.08323/) (2018)
- [Variational inference formulation for a model-free simulation of a dynamical system with unknown parameters by a recurrent neural network](https://mlsanity.com/paper/2003.01184/) (2020)

## Built on by (most cited first, 2 of 2)

- [An End-to-End Time Series Model for Simultaneous Imputation and Forecast](https://mlsanity.com/paper/2306.00778/) (2023)
- [Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks](https://mlsanity.com/paper/2305.15920/) (2023)

## Abstract (arXiv)

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.