51 citations · 78 across the 7 of their papers we have counts for
6 papers · 1 filter
Learning a Reduced Basis of Dynamical Systems using an Autoencoder
David Sondak, Pavlos Protopapas
Machine learning models have emerged as powerful tools in physics and engineering. Although flexible, a fundamental challenge remains on how to connect new machine learning models…
Unsupervised Learning of Solutions to Differential Equations with Generative Adversarial Networks
Dylan Randle, Pavlos Protopapas, David Sondak
Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neur…
Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection
Parvathi Kooloth, David Sondak, Leslie M. Smith
For two-dimensional Rayleigh-Bénard convection, classes of unstable, steady solutions were previously computed using numerical continuation (Waleffe, 2015; Sondak, 2015). The `prim…
Solving Differential Equations Using Neural Network Solution Bundles
Cedric Flamant, Pavlos Protopapas, David Sondak
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approach…
High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection
David Sondak, Thomas M. Smith, Roger P. Pawlowski +2
The variational multiscale (VMS) formulation is used to develop residual-based VMS large eddy simulation (LES) models for Rayleigh-Bénard convection. The resulting model is a mixed…
Hamiltonian neural networks for solving equations of motion
Marios Mattheakis, David Sondak, Akshunna S. Dogra +1
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that gover…