Accurate prediction of dynamical systems in unstructured meshes has recently shown successes in scientific simulations. Many dynamical systems have a nonnegligible level of stochasticity introduced by various factors (e.g. chaoticity), so there is a need for a unified framework that captures both deterministic and stochastic components in the rollouts of these systems. Inspired by regeneration learning, we propose a new model that combines generative and sequential networks to model dynamical systems. Specifically, we use an autoencoder to learn compact representations of full-space physical variables in a low-dimensional space. We then integrate a transformer with a conditional normalizing flow model to model the temporal sequence of latent representations. We evaluate the new model in both deterministic and stochastic systems. The model outperforms several competitive baseline models and makes more accurate predictions of deterministic systems. Its own prediction error is also reflected in its uncertainty estimations. When predicting stochastic systems, the proposed model generates high-quality rollout samples. The mean and variance of these samples well match the statistics of samples computed from expensive numerical simulations.

We present SSR-VFD, a novel deep learning framework that produces coherent spatial super-resolution (SSR) of three-dimensional vector field data (VFD). SSR-VFD is the first work that advocates a machine learning approach to generate high-resolution vector fields from low-resolution ones. The core of SSR-VFD lies in the use of three separate neural nets that take the three components of a low-resolution vector field as input and jointly output a synthesized high-resolution vector field. To capture spatial coherence, we take into account magnitude and angle losses in network optimization. Our method can work in the in situ scenario where VFD are down-sampled at simulation time for storage saving and these reduced VFD are upsampled back to their original resolution during postprocessing. To demonstrate the effectiveness of SSR-VFD, we show quantitative and qualitative results with several vector field data sets of different characteristics and compare our method against volume upscaling using bicubic interpolation, and two solutions based on CNN and GAN, respectively.