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math.AP2020
Data assimilation for the Navier-Stokes equations using local observables
Animikh Biswas, Zachary Bradshaw, Michael S. Jolly
We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations…
math.AP2020
Error Estimates for Deep Learning Methods in Fluid Dynamics
Animikh Biswas, Jing Tian, Suleyman Ulusoy
In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes e…
math.AP2020
Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations
Animikh Biswas, Randy Price
In this paper, we provide conditions, \emph{based solely on the observed data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation…