Accurate generation of stochastic dynamics based on multi-model generative adversarial networks

Area of Science:

• Statistical mechanics
• Machine learning
• Stochastic processes

Background:

• Generative Adversarial Networks (GANs) show promise in data generation.
• Recent efforts explore GANs for statistical-mechanics models.
• Quantitative testing on a lattice stochastic process is needed.

Purpose of the Study:

• To quantitatively evaluate GANs for statistical-mechanics models.
• To improve the accuracy of GANs in modeling stochastic processes.
• To address challenges in GAN convergence and trajectory generation.

Main Methods:

• Applied GANs to a prototypical lattice stochastic process.
• Introduced noise to training data to stabilize Generator and Discriminator losses.
• Implemented a multi-model GAN procedure with random Generator selection for trajectory generation.

Main Results:

• Achieved near-ideal Generator and Discriminator loss values.
• Preserved the discrete nature of the model despite noise.
• The multi-model approach significantly increased accuracy in predicting equilibrium and escape-time distributions.
• Observed persistent oscillations typical of adversarial training.

Conclusions:

• GANs are a promising tool for complex statistical dynamics.
• Noise injection and multi-model strategies enhance GAN performance in this domain.
• Further research can leverage GANs for advanced machine learning in physics.