Model Reduction Techniques for Large-scale PDE Data Compression

Abstract: The future of high-performance computing will presumably see memory capacity and bandwidth fail to keep pace with data generated, for instance, from massively parallel partial differential equation (PDE) systems.  Current strategies proposed to address this bottleneck entail the omission of large fractions of data, as well as the incorporation of in situ compression algorithms to avoid overuse of memory.  To ensure that post-processing operations are successful, this must be done in a way that a sufficiently accurate representation of the solution is stored.  Moreover, in situations where the input/output system becomes a bottleneck in analysis, visualization, etc., or the execution of the PDE solver is expensive, the number of passes made over the data must be minimized.

Motivated by this big-data challenge, in this talk, I will present scalable low-rank factorization algorithms for data reduction associated with large-scale PDE simulations.  An emphasis of these algorithms has been to use coarse representations of the data, i.e., sketches, compatible with the PDE discretization grid, as well as random projections to accelerate the construction of the low-rank factorization.  Using this framework, I will illustrate compression factors exceeding 100 − 400 on turbulent flow data, while maintaining accuracy with respect to first- and second-order flow statistics.  As a result, these methods have the potential to deliver real-time insight on solution dynamics to application domain experts and enable post-processing operations involving high-dimensional, full PDE solution ensembles, such as design adaptation/optimization, model calibration and inference, as well as uncertainty propagation.  A nonlinear extension of these linear compression algorithms along with numerical examples will also be presented.

Speaker’s Bio: Alireza Doostan is a Professor in the Aerospace Engineering Sciences Department at the University of Colorado-Boulder (CU-Boulder) and an affiliated faculty of the Applied Mathematics Department.  From 2018 to 2021 he served as the director of the Aerospace Mechanics Research Center.  Prior to his appointment at CU-Boulder in 2010, he was an Engineering Research Associate at the Center for Turbulence Research at Stanford University.  Alireza received his Ph.D. in Structural Engineering and M.A. in Applied Mathematics and Statistics from Johns Hopkins University both in 2007.  He is a recipient of a Department of Energy (Advanced Scientific Computer Research) and a National Science Foundation (Engineering Design) Early Career award, as well as multiple teaching awards from CU-Boulder and the American Institute of Aeronautics and Astronautics.  His research interests include uncertainty quantification, reduced order and data-driven modeling, optimization under uncertainty, machine learning, and computational stochastic mechanics.