5 papers · 1 filter
A review of shape-morphing solutions and evolutional neural networks for spatiotemporal dynamics
Mohammad Farazmand
Shape-morphing solutions (SMS) refer to a class of approximate solutions of partial differential equations (PDEs) with the distinguishing feature that they depend nonlinearly on a…
Discrete Empirical Interpolation Method with Upper and Lower Bound Constraints
Louisa B. Ebby, Mohammad Farazmand
Discrete Empirical Interpolation Method (DEIM) is a simple and effective method for reconstructing a function from its incomplete pointwise observations. However, applying DEIM to…
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…
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…
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…