Journal ArticleSDYN-GANs: Adversarial learning methods for multistep generative models for general order stochastic dynamicsStinis, P; Daskalakis, C; Atzberger, PJWe introduce adversarial learning methods for data-driven generative modeling of 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. From observations of trajectory samples, we introduce methods for learning long-time predictors and stable representations of the dynamics. Our approaches use discriminators based on Maximum Mean Discrepancy (MMD), training protocols using both 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. Our adversarial learning approaches provide methods for obtaining stable generative models for dynamic tasks including long-time prediction and developing simulations for stochastic systems.Elsevier2024-12-0110611634Journal of Computational Physics519C1134420021-9991https://doi.org/10.1016/j.jcp.2024.1134422306101Machine LearningGenerative AIAdversarial LearningStochastic ProcessesDynamical SystemsData-Driven ModelingScientific ComputationNational Science Foundation