8 citations · 9 across the 5 of their papers we have counts for
5 papers
Fisher information and shape-morphing modes for solving the Fokker-Planck equation in higher dimensions
William Anderson, Mohammad Farazmand
The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this…
Fast and scalable computation of shape-morphing nonlinear solutions with application to evolutional neural networks
William Anderson, Mohammad Farazmand
We develop fast and scalable methods for computing reduced-order nonlinear solutions (RONS). RONS was recently proposed as a framework for reduced-order modeling of time-dependent…
Shape-morphing reduced-order models for nonlinear Schrodinger equations
William Anderson, Mohammad Farazmand
We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling meth…
Evolution of nonlinear reduced-order solutions for PDEs with conserved quantities
William Anderson, Mohammad Farazmand
Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-develope…
Comparison of Two Scale-Dependent Dynamic Subgrid-Scale Models for Simulations of Neutrally Buoyant Shear-Driven Atmospheric Boundary Layer Flows
William Anderson, Sukanta Basu, Chris Letchford
A new scale-dependent dynamic subgrid-scale (SGS) model based on Kolmogorov's scaling hypothesis is presented. This SGS model is utilized in large-eddy simulation of a well-known c…