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Explore a 59-minute lecture on CUR Matrix Decomposition for Scalable Reduced-Order Modeling of Nonlinear Partial Differential Equations using Time-Dependent Bases. Delve into dynamical low-rank approximation (DLRA) techniques for solving high-dimensional partial differential equations by extracting multi-dimensional correlations. Learn about an adaptive sparse interpolation algorithm based on CUR matrix decomposition that enables time-dependent basis (TDB) reduced-order models to achieve computational efficiency for generic nonlinear PDEs. Discover how this approach reduces implementation efforts and intrusiveness when applying TDB-based ROMs to new PDEs. Examine a rank-adaptive strategy for controlling low-rank approximation errors as systems evolve. Gain insights into applications in turbulent combustion and uncertainty propagation from Assistant Professor Hessam Babaee of the University of Pittsburgh, an expert in reduced-order modeling and machine learning techniques for science and engineering problems.
