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As an alternative to the popular balanced truncation method, the cross Gramian matrix induces a class of balancing model reduction techniques. Besides the classical computation of the cross Gramian by a Sylvester matrix equation, an…

Optimization and Control · Mathematics 2016-06-14 Christian Himpe , Mario Ohlberger

We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without…

Numerical Analysis · Mathematics 2021-10-26 Ion Victor Gosea , Serkan Gugercin , Christopher Beattie

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Machine Learning · Statistics 2017-12-08 Luca Ambrogioni , Eric Maris

Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Elnaz Rezaian , Cheng Huang , Karthik Duraisamy

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…

Optimization and Control · Mathematics 2013-03-19 Mihaly Petreczky , Rafael Wisniewski , John Leth

A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

This work introduces the empirical cross gramian for multiple-input-multiple-output systems. The cross gramian is a tool for reducing the state space of control systems, which conjoins controllability and observability information into a…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…

Optimization and Control · Mathematics 2019-01-29 Xiaodong Cheng , Jacquelien M. A. Scherpen , Bart Besselink

Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…

Computation · Statistics 2014-05-22 Jim E. Griffin

We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…

Optimization and Control · Mathematics 2017-05-02 Peter Benner , Pawan Goyal

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…

Machine Learning · Statistics 2021-10-27 Benjamin Kurt Miller , Alex Cole , Patrick Forré , Gilles Louppe , Christoph Weniger

Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…

Optimization and Control · Mathematics 2019-09-11 Peter Benner , Pawan Goyal , Igor Pontes Duff

This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject…

Optimization and Control · Mathematics 2017-08-15 Dany Abou Jaoude , Mazen Farhood

Measures characterizing the non-Markovianity degree of the quantum dynamics have several drawbacks when applied to real devices. They depend on the chosen measurement time interval and are highly sensitive to experimental noise and errors.…

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard…

Systems and Control · Computer Science 2016-06-08 Andrew W. Palmer , Andrew J. Hill , Steven J. Scheding

Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the…

Quantum Physics · Physics 2019-10-02 Marco G. Genoni , Tommaso Tufarelli

A fast algorithm for the large-scale joint inversion of gravity and magnetic data is developed. It uses a nonlinear Gramian constraint to impose correlation between density and susceptibility of reconstructed models. The global objective…

In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…

Systems and Control · Computer Science 2017-09-27 Enoch Yeung , Zhiyuan Liu , Nathan O. Hodas

Many methods for estimating integrated volatility and related functionals of semimartingales in the presence of jumps require specification of tuning parameters for their use in practice. In much of the available theory, tuning parameters…

Statistics Theory · Mathematics 2024-10-23 B. Cooper Boniece , José E. Figueroa-López , Yuchen Han

We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…

Numerical Analysis · Mathematics 2022-12-16 Rami Katz , Yoel Shkolnisky