# Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2305.15920 · HTML: https://mlsanity.com/paper/2305.15920/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Generative Adversarial Network in Medical Imaging: A Review](https://mlsanity.com/paper/1809.07294/) (2018)
- [C-RNN-GAN: Continuous recurrent neural networks with adversarial training](https://mlsanity.com/paper/1611.09904/) (2016)
- [The Numerics of GANs](https://mlsanity.com/paper/1705.10461/) (2017)
- [Generative Adversarial Networks (GANs Survey): Challenges, Solutions, and Future Directions](https://mlsanity.com/paper/2005.00065/) (2020)
- [Generative adversarial networks (GAN) based efficient sampling of chemical space for inverse design of inorganic materials](https://mlsanity.com/paper/1911.05020/) (2019)
- [Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks](https://mlsanity.com/paper/1803.08182/) (2018)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System](https://mlsanity.com/paper/2111.03126/) (2021)

## Built on by (most cited first, 1 of 1)

- [Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks](https://mlsanity.com/paper/2507.21763/) (2025)

## Abstract (arXiv)

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test this approach by applying it to a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. Importantly, the discreteness of the model is retained despite the noise. As typical for adversarial approaches, oscillations around the convergence limit persist also at large epochs. This undermines model selection and the quality of the generated trajectories. We demonstrate that a simple multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. This is illustrated by quantitative analysis of both the predicted equilibrium probability distribution and of the escape-time distribution. Based on the reported findings, we believe that GANs are a promising tool to tackle complex statistical dynamics by machine learning techniques