6 papers
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…
Rapid estimation of global sea surface temperatures from sparse streaming in situ observations
Cassidy All, Kevin Ho, Maya Magnuski +3
Reconstructing high-resolution sea surface temperatures (SST) from staggered SST measurements is essential for weather forecasting and climate projections. However, when SST measur…
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…
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…