1.5k citations · 2.9k across the 12 of their papers we have counts for
12 papers
Computationally Efficient Data-Driven Discovery and Linear Representation of Nonlinear Systems For Control
Madhur Tiwari, George Nehma, Bethany Lusch
This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed met…
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…
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…
Deep learning for universal linear embeddings of nonlinear dynamics
Bethany Lusch, J. Nathan Kutz, Steven L. Brunton
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the…
Modeling cognitive deficits following neurodegenerative diseases and traumatic brain injuries with deep convolutional neural networks
Bethany Lusch, Jake Weholt, Pedro D. Maia +1
The accurate diagnosis and assessment of neurodegenerative disease and traumatic brain injuries (TBI) remain open challenges. Both cause cognitive and functional deficits due to fo…
Shape Constrained Tensor Decompositions using Sparse Representations in Over-Complete Libraries
Bethany Lusch, Eric C. Chi, J. Nathan Kutz
We consider -way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. O…
Submodular Hamming Metrics
Jennifer Gillenwater, Rishabh Iyer, Bethany Lusch +2
We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tract…