Nonlinear model order reduction via Dynamic Mode Decomposition

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix that correlates spatial features while simultaneously associating the activity with periodic temporal behavior. With this decomposition, one can obtain a fully reduced dimensional surrogate model and avoid the evaluation of the nonlinear term in the online stage. This allows for an impressive speed up of the computational cost, and, at the same time, accurate approximations of the problem. We present a suite of numerical tests to illustrate our approach and to show the effectiveness of the method in comparison to existing approaches

A single antenna ambient noise cancellation method for in-situ radiated EMI measurements in the time-domain

This paper presents a single antenna ambient noise cancellation method for in-situ radiated emissions measurements performed using an entirely time-domain approach and the sliding window Empirical Mode Decomposition. The method requires a pair of successive measurements, an initial one for characterizing the ambient noise and a final one for the EMI measurement in the presence of ambient noise. The method assumes the spectral content of the ambient noise is stable between both measurements. The measured time-domain EMI is decomposed into a finite set of intrinsic mode functions. Some modes contain the ambient noise signals while other modes contain the actual components of the EMI. A brute-force search algorithm determines which mode, or combination of modes, maximize the absolute difference between the magnitude of their spectrum and the ambient noise levels for every frequency bin in the measurement bandwidth. Experimental results show the effectiveness of this method for attenuating several ambient noise signals in the 30 MHz – 1 GHz band.Postprint (published version

Fast and Guaranteed Tensor Decomposition via Sketching

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results.Comment: 29 pages. Appeared in Proceedings of Advances in Neural Information Processing Systems (NIPS), held at Montreal, Canada in 201