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Data Assimilation in Chaotic Systems Using Deep Reinforcement Learning
A prime example is the widely used ensemble Kalman filter (EnKF), which relies on linear updates to minimize variance among the ensemble of forecast states.
Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era
Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing.
Continuous data assimilation with blurred-in-time measurements of the surface quasi-geostrophic equation
An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time.
Analysis of PDEs Optimization and Control 35Q35, 35Q86, 35Q93, 37B55, 74H40, 93B52
