Weak-SINDy Surrogate Models and Their Application in Streaming Scientific Data Compression

Abstract:
In recent years, several sparse-regression-based techniques, such as Sparse Identification of Nonlinear Dynamics (SINDy), weak-SINDy, and operator regression methods, have been developed for system identification and surrogate modeling from data.  These methods express the system dynamics as linear combinations of a prescribed set of basis functions/operators and compute the coefficients via solving a linear system built from data.  In this talk, we will introduce the weak-SINDy method for constructing surrogate models, present the error analysis for weak-SINDy surrogate models, and discuss a new streaming data compression method based on weak-SINDy surrogates.  This compression method utilizes the variational formulation in weak-SINDy to reduce the memory footprint during compression.  Therefore, it is well-suited to be applied in the streaming scenario, in which storing the full data set offline is often infeasible.

Speaker’s Bio:
Dr. Paul Laiu is a Staff Mathematician in the Multiscale Methods and Dynamics Group at Oak Ridge National Laboratory.  He received his Ph.D. degree in Electrical and Computer Engineering from University of Maryland College Park in 2016.  Paul’s research interest includes surrogate modeling, iterative solvers, and numerical schemes for various partial differential equations in kinetic theory.  His work focuses on the design, development, and analysis of mathematical tools that accelerate the simulation and learning of multiscale systems, with applications in astrophysics, computational fluid dynamics, cybersecurity, health, and rarefied gas.