Data reduction through compression is emerging as a promising approach to ease I/O costs for simulation codes on supercomputers. Typically, this compression is achieved by techniques that operate on individual time slices. However, as simulation codes advance in time, outputting multiple time slices as they go, the opportunity for compression incorporating the time dimension has not been extensively explored. Moreover, recent supercomputers are increasingly equipped with deeper memory hierarchies, including solid state drives and burst buffers, which creates the opportunity to temporarily store multiple time slices and then apply compression to them all at once, i.e., spatiotemporal compression. This paper explores the benefits of incorporating the time dimension into existing wavelet compression, including studying its key parameters and demonstrating its benefits in three axes: storage, accuracy, and temporal resolution. Our results demonstrate that temporal compression can improve each of these axes, and that the impact on performance for real systems, including tradeoffs in memory usage and execution time, is acceptable. We also demonstrate the benefits of spatiotemporal wavelet compression with real-world visualization use cases and tailored evaluation metrics.

Based on physical laws describing the multiscale structure of turbulent flows, this paper proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian perspective, an algorithm is proposed to jointly estimate motion, regularization hyperparameters, and to select the most likely physical prior among a set of models. Hyperparameter and model inference are conducted by posterior maximization, obtained by marginalizing out non--Gaussian motion variables. The Bayesian estimator is assessed on several image sequences depicting synthetic and real turbulent fluid flows. Results obtained with the proposed approach exceed the state-of-the-art results in fluid flow estimation.

Numerical simulations of turbulent fluid flow in areas ranging from solar physics to aircraft design are dominated by the presence of repeating patterns known as coherent structures. These persistent features are not yet well understood, but are believed to play an important role in the dynamics of turbulent fluid motion, and are the subject of study across numerous scientific and engineering disciplines. To facilitate their investigation a variety of techniques have been devised to track the paths of these structures as they evolve through time. Heretofore, all such feature tracking methods have largely ignored the physics governing the motion of these objects at the expense of error prone and often computationally expensive solutions. In this paper, we present a feature path prediction method that is based on the physics of the underlying solutions to the equations of fluid motion. To the knowledge of the authors the accuracy of these predictions is superior to methods reported elsewhere. Moreover, the precision of these forecasts for many applications is sufficiently high to enable the use of only the most rudimentary and inexpensive forms of correspondence matching. We also provide insight on the relationship between the internal time stepping used in a CFD simulation, and the evolution of coherent structures, that we believe is of benefit to any feature tracking method applicable to CFD. Finally, our method is easy to implement, and computationally inexpensive to execute, making it well suited for very high-resolution simulations.

Based on scaling laws describing the statistical structure of turbulent motion across scales, we propose a multiscale and non-parametric regularizer for optic-flow estimation. Regularization is achieved by constraining motion increments to behave through scales as the most likely self-similar process given some image data. In a first level of inference, the hard constrained minimization problem is optimally solved by taking advantage of lagrangian duality. It results in a collection of first-order regularizers acting at different scales. This estimation is non-parametric since the optimal regularization parameters at the different scales are obtained by solving the dual problem. In a second level of inference, the most likely self-similar model given the data is optimally selected by maximization of Bayesian evidence. The motion estimator accuracy is first evaluated on a synthetic image sequence of simulated bi-dimensional turbulence and then on a real meteorological image sequence. Results obtained with the proposed physical based approach exceeds the best state of the art results. Furthermore, selecting from images the most evident multiscale motion model enables the recovery of physical quantities, which are of major interest for turbulence characterization.