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

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