1.5k citations · 2.9k across the 12 of their papers we have counts for
5 papers · 1 filter
Deep Learning Models for Global Coordinate Transformations that Linearize PDEs
Craig Gin, Bethany Lusch, Steven L. Brunton +1
We develop a deep autoencoder architecture that can be used to find a coordinate transformation which turns a nonlinear PDE into a linear PDE. Our architecture is motivated by the…
Using recurrent neural networks for nonlinear component computation in advection-dominated reduced-order models
Romit Maulik, Vishwas Rao, Sandeep Madireddy +2
Rapid simulations of advection-dominated problems are vital for multiple engineering and geophysical applications. In this paper, we present a long short-term memory neural network…
A turbulent eddy-viscosity surrogate modeling framework for Reynolds-Averaged Navier-Stokes simulations
Romit Maulik, Himanshu Sharma, Saumil Patel +2
The Reynolds-averaged Navier-Stokes (RANS) equations for steady-state assessment of incompressible turbulent flows remain the workhorse for practical computational fluid dynamics (…
Time-series learning of latent-space dynamics for reduced-order model closure
Romit Maulik, Arvind Mohan, Bethany Lusch +3
We study the performance of long short-term memory networks (LSTMs) and neural ordinary differential equations (NODEs) in learning latent-space representations of dynamical equatio…
Data-driven discovery of coordinates and governing equations
Kathleen Champion, Bethany Lusch, J. Nathan Kutz +1
The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse…