117 citations · 378 across the 17 of their papers we have counts for
17 papers
Recent Advances of NeuroDiffEq -- An Open-Source Library for Physics-Informed Neural Networks
Shuheng Liu, Pavlos Protopapas, David Sondak +1
Solving differential equations is a critical challenge across a host of domains. While many software packages efficiently solve these equations using classical numerical approaches…
Extending a Physics-Informed Machine Learning Network for Superresolution Studies of Rayleigh-Bénard Convection
Diane M. Salim, Blakesley Burkhart, David Sondak
Advancing our understanding of astrophysical turbulence is bottlenecked by the limited resolution of numerical simulations that may not fully sample scales in the inertial range. M…
DEQGAN: Learning the Loss Function for PINNs with Generative Adversarial Networks
Blake Bullwinkel, Dylan Randle, Pavlos Protopapas +1
Solutions to differential equations are of significant scientific and engineering relevance. Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving…
Multi-Task Learning based Convolutional Models with Curriculum Learning for the Anisotropic Reynolds Stress Tensor in Turbulent Duct Flow
Haitz Sáez de Ocáriz Borde, David Sondak, Pavlos Protopapas
The Reynolds-averaged Navier-Stokes (RANS) equations require accurate modeling of the anisotropic Reynolds stress tensor. Traditional closure models, while sophisticated, often onl…
Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems
Shaan Desai, Marios Mattheakis, David Sondak +2
Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms…
Convolutional Neural Network Models and Interpretability for the Anisotropic Reynolds Stress Tensor in Turbulent One-dimensional Flows
Haitz Sáez de Ocáriz Borde, David Sondak, Pavlos Protopapas
The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in turbulence applications. They require accurately modeling the anisotropic Reynolds stress tensor, for which…
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…
Neural Network Models for the Anisotropic Reynolds Stress Tensor in Turbulent Channel Flow
Rui Fang, David Sondak, Pavlos Protopapas +1
Reynolds-averaged Navier-Stokes (RANS) equations are presently one of the most popular models for simulating turbulence. Performing RANS simulation requires additional modeling for…
Deep learning for turbulent channel flow
Rui Fang, David Sondak, Pavlos Protopapas +1
Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and n…
Can phoretic particles swim in two dimensions?
David Sondak, Cory Hawley, Siyu Heng +3
Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be…
Optimal Heat Transport in Rayleigh-Bénard Convection
David Sondak, Leslie M. Smith, Fabian Waleffe
Steady flows that optimize heat transport are obtained for two-dimensional Rayleigh-Bénard convection with no-slip horizontal walls for a variety of Prandtl numbers and Raylei…
A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics
David Sondak, John N. Shadid, Assad A. Oberai +3
New large eddy simulation (LES) turbulence models for incompressible magnetohydrodynamics (MHD) derived from the variational multiscale (VMS) formulation for finite element simulat…