71 citations · 112 across the 22 of their papers we have counts for
5 papers · 1 filter
Bootstrapping the Operator Norm in High Dimensions: Error Estimation for Covariance Matrices and Sketching
Miles E. Lopes, N. Benjamin Erichson, Michael W. Mahoney
Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm.…
Randomized methods to characterize large-scale vortical flow network
Zhe Bai, N. Benjamin Erichson, Muralikrishnan Gopalakrishnan Meena +2
We demonstrate the effective use of randomized methods for linear algebra to perform network-based analysis of complex vortical flows. Network theoretic approaches can reveal the c…
Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction
N. Benjamin Erichson, Michael Muehlebach, Michael W. Mahoney
In addition to providing high-profile successes in computer vision and natural language processing, neural networks also provide an emerging set of techniques for scientific proble…
JumpReLU: A Retrofit Defense Strategy for Adversarial Attacks
N. Benjamin Erichson, Zhewei Yao, Michael W. Mahoney
It has been demonstrated that very simple attacks can fool highly-sophisticated neural network architectures. In particular, so-called adversarial examples, constructed from pertur…
Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
N. Benjamin Erichson, Lionel Mathelin, Zhewei Yao +3
In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose…