101 citations · 166 across the 9 of their papers we have counts for
10 papers
Estimating Hierarchically Rank Structured Covariance Matrices
Robin Armstrong, Anil Damle, Samuel E. Otto
We consider the problem of estimating a high-dimensional covariance matrix from a very limited number of samples. This problem is ubiquitous in computational fluid dynamics, where…
Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders
Samuel E. Otto, Gregory R. Macchio, Clarence W. Rowley
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach fo…
Learning Bilinear Models of Actuated Koopman Generators from Partially-Observed Trajectories
Samuel E. Otto, Sebastian Peitz, Clarence W. Rowley
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature l…
Model Reduction for Nonlinear Systems by Balanced Truncation of State and Gradient Covariance
Samuel E. Otto, Alberto Padovan, Clarence W. Rowley
Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance becaus…
Optimizing Oblique Projections for Nonlinear Systems using Trajectories
Samuel E. Otto, Alberto Padovan, Clarence W. Rowley
Reduced-order modeling techniques, including balanced truncation and -optimal model reduction, exploit the structure of linear dynamical systems to produce models th…
Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems; a New Approach Using Secants
Samuel E. Otto, Clarence W. Rowley
Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable…
Data-Driven Model Predictive Control using Interpolated Koopman Generators
Sebastian Peitz, Samuel E. Otto, Clarence W. Rowley
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserv…
Analysis of amplification mechanisms and cross-frequency interactions in nonlinear flows via the harmonic resolvent
Alberto Padovan, Samuel E. Otto, Clarence W. Rowley
We propose a framework that elucidates the input-output characteristics of flows with complex dynamics arising from nonlinear interactions between different time scales. More speci…
A Discrete Empirical Interpolation Method for Interpretable Immersion and Embedding of Nonlinear Manifolds
Samuel E. Otto, Clarence W. Rowley
Manifold learning techniques seek to discover structure-preserving mappings of high-dimensional data into low-dimensional spaces. While the new sets of coordinates specified by the…
Linearly-Recurrent Autoencoder Networks for Learning Dynamics
Samuel E. Otto, Clarence W. Rowley
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator.…