2 citations · 2 across the 2 of their papers we have counts for
6 papers
Non-autoregressive time-series methods for stable parametric reduced-order models
Romit Maulik, Bethany Lusch, Prasanna Balaprakash
Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accur…
Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders
Romit Maulik, Bethany Lusch, Prasanna Balaprakash
A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced…
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…