DDPS | “Reducing Data Resolution for better Reconstruction: Super-Resolution of Navier-Stokes Flows” скачать в хорошем качестве

DDPS | “Reducing Data Resolution for better Reconstruction: Super-Resolution of Navier-Stokes Flows”

DDPS Talk date: February 28th, 2025 Speaker: Kyongmin Yeo (IBM T.J. Watson Research Center, https://www.dam.brown.edu/people/kyeo/) Description: Super-resolution (SR) refers to the problem of reconstructing high-resolution information from low-resolution data. Recently, SR of physical system has attracted great attention due to its potential in real-life applications. While SR for physical systems has shown promising results empirically, theoretical understanding on the behavior of SR is far from complete. In this study, we aim to provide theoretical analysis of SR for noisy observations. We consider a SR method to reconstruct the ground-truth state of 2-D Navier-Stokes (NS) flows from noisy observations. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing resolution and, then, a dynamic observer is employed to reconstruct the flow field by reversing back the lost information. We provide a theoretical analysis, which indicates a chaos synchronization of the SR observer with the ground-truth NS sytsem. It is shown that, even with noisy observations, the SR observer converges toward the ground-truth NS flow exponentially fast, and the deviation of the observer from the reference system is bounded. Counter-intuitively, our theoretical analysis shows that the deviation can be reduced by increasing the length scale of the spatial average, i.e., making the resolution coarser. The theoretical analysis is confirmed by numerical experiments of two-dimensional NS flows. The numerical experiments suggest that there is a critical length scale for the spatial average, below which making the resolution coarser improves the reconstruction. Bio: Dr. Yeo is a Research Scientist at IBM T.J. Watson Research Center. He received a Ph.D in Applied Mathematics from Brown University in 2011. Before joining IBM Research in 2013, he was a postdoctoral fellow at the Lawrence Berkeley National Lab. Dr. Yeo has been working on a range of research areas, from soft matter physics to atmospheric sciences. Since joining IBM Research, his research interest has been focused on hybrid physics-statistics models and deep learning for random dynamical systems. DDPS webinar: https://www.librom.net/ddps.html 💻 LLNL News: https://www.llnl.gov/news 📲 Instagram:   / livermore_lab   🤳 Facebook:   / livermore.lab   🐤 Twitter:   / livermore_lab   About LLNL: Lawrence Livermore National Laboratory has a mission of strengthening the United States’ security through development and application of world-class science and technology to: 1) enhance the nation’s defense, 2) reduce the global threat from terrorism and weapons of mass destruction, and 3) respond with vision, quality, integrity and technical excellence to scientific issues of national importance. Learn more about LLNL: https://www.llnl.gov/. IM release number is: LLNL-VIDEO-872787