SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics
This work addresses the challenge of modeling complex stochastic dynamics for physical systems, offering incremental improvements in generative modeling techniques.
The paper tackles the problem of data-driven generative modeling for nth-order stochastic dynamics by introducing adversarial learning methods based on GANs with stable m-step stochastic numerical integrators, resulting in stable generative models for tasks like long-time prediction and simulation of stochastic systems.
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.