3 papers
math.NA2025
Bridging the Gap Between Deterministic and Probabilistic Approaches to State Estimation
Lev Kakasenko, Alen Alexanderian, Mohammad Farazmand +1
We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of…
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…