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math.NA2024
Sequential data assimilation for PDEs using shape-morphing solutions
Zachary T. Hilliard, Mohammad Farazmand
Shape-morphing solutions (also known as evolutional deep neural networks, reduced-order nonlinear solutions, and neural Galerkin schemes) are a new class of methods for approximati…
math.DS2024
State Estimation Using Sparse DEIM and Recurrent Neural Networks
Mohammad Farazmand
Sparse Discrete Empirical Interpolation Method (S-DEIM) was recently proposed for state estimation in dynamical systems when only a sparse subset of the state variables can be obse…
math.NA2024
Sparse Discrete Empirical Interpolation Method: State Estimation from Few Sensors
Mohammad Farazmand
Discrete empirical interpolation method (DEIM) estimates a function from its incomplete pointwise measurements. Unfortunately, DEIM suffers large interpolation errors when few meas…