SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics

TL;DR

This paper presents adversarial learning methods for modeling the dynamics of high-order stochastic systems using GANs with stable numerical integrators, enabling accurate long-term predictions and system simulations.

Contribution

It introduces novel GAN-based frameworks for learning stochastic dynamics with stable integrators, including MMD-based discriminators and multi-scale response modeling.

Findings

Effective modeling of physical systems' force-laws and noise parameters.

Stable long-term predictions of stochastic dynamics.

Versatile methods for dynamic response over various time-scales.

Abstract

We introduce adversarial learning methods for data-driven generative modeling of the dynamics of $n^{th}$-order stochastic systems. Our approach builds on Generative Adversarial Networks (GANs) with generative model classes based on stable $m$-step stochastic numerical integrators. We introduce different formulations and training methods for learning models of stochastic dynamics based on observation of trajectory samples. We develop approaches using discriminators based on Maximum Mean Discrepancy (MMD), training protocols using conditional and marginal distributions, and methods for learning dynamic responses over different time-scales. We show how our approaches can be used for modeling physical systems to learn force-laws, damping coefficients, and noise-related parameters. The adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.