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Quantum-inspired singular value decomposition (SVD) is a technique to perform SVD in logarithmic time with respect to the dimension of a matrix, given access to the matrix embedded in a segment-tree data structure. The speedup is possible…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
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…
A unified model of voltage mode control (VMC) and current mode control (CMC) is proposed to predict the saddle-node bifurcation (SNB). Exact SNB boundary conditions are derived, and can be further simplified in various forms for design…
To implement deep learning models on edge devices, model compression methods have been widely recognized as useful. However, it remains unclear which model compression methods are effective for Structured State Space Sequence (S4) models…
Modern data analysis increasingly requires identifying shared latent structure across multiple high-dimensional datasets. A commonly used model assumes that the data matrices are noisy observations of low-rank matrices with a shared…
Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…
The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…
With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which…
For linearly constrained least-squares problems that depend on a vector of parameters, this paper proposes techniques for reducing the number of involved optimization variables. After first eliminating equality constraints in a numerically…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
Deep learning models incorporating linear SSMs have gained attention for capturing long-range dependencies in sequential data. However, their large parameter sizes pose challenges for deployment on resource-constrained devices. In this…
In this work, the application of the multi-dimensional higher order dynamic mode decomposition (HODMD) is proposed for the first time to analyse combustion databases. In particular, HODMD has been adapted and combined with other…
With the abundance of data in recent years, interesting challenges are posed in the area of recommender systems. Producing high quality recommendations with scalability and performance is the need of the hour. Singular Value…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
Our world is full of physics-driven data where effective mappings between data manifolds are desired. There is an increasing demand for understanding combined model-based and data-driven methods. We propose a nonlinear, learned singular…
Given multiple time series data, how can we efficiently find latent patterns in an arbitrary time range? Singular value decomposition (SVD) is a crucial tool to discover hidden factors in multiple time series data, and has been used in many…
Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…