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math.DS2023
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
Matthew J. Colbrook, Qin Li, Ryan V. Raut +1
Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectra…
math.NA2023
On optimal bases for multiscale PDEs and Bayesian homogenization
Shi Chen, Zhiyan Ding, Qin Li +1
PDE solutions are numerically represented by basis functions. Classical methods employ pre-defined bases that encode minimum desired PDE properties, which naturally cause redundant…