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.

翻译：我们引入了针对 $n$ 阶随机系统动力学的数据驱动生成建模的对抗学习方法。我们的方法基于生成对抗网络（GANs），其生成模型类别建立在稳定的 $m$ 步随机数值积分器上。我们提出了基于轨迹样本观测来学习随机动力学模型的不同公式和训练方法。我们开发了基于最大平均差异（MMD）的判别器方法、使用条件分布和边际分布的训练协议，以及在不同时间尺度上学习动态响应的方法。我们展示了如何将这些方法用于物理系统建模，以学习力定律、阻尼系数和噪声相关参数。这些对抗学习方法为包括长时间预测在内的动态任务提供了获取稳定生成模型的途径，并可用于开发随机系统的仿真。