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Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present…

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…

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…

We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess…

Proper orthogonal decomposition (POD) allows reduced-order modeling of complex dynamical systems at a substantial level, while maintaining a high degree of accuracy in modeling the underlying dynamical systems. Advances in machine learning…

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…

This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…

The minimum realization problem of hidden Markov models (HMM's) is a fundamental question of stationary discrete-time processes with a finite alphabet. It was shown in the literature that tensor decomposition methods give the hidden Markov…

Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…

This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…

The model reduction problem for high-order multi-input, multi-output (MIMO) polynomial nonlinear systems based on moment matching is addressed. The technique of power-series decomposition is exploited: this decomposes the solution of the…

We introduce a framework for model reduction of chain models for dissipative particle dynamics (DPD) simulations, where the characteristic size of the chain, pressure, density, and temperature are preserved. The proposed methodology reduces…

Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

Dimensionality reduction for high-order tensors is a challenging problem. In conventional approaches, higher order tensors are `vectorized` via Tucker decomposition to obtain lower order tensors. This will destroy the inherent high-order…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…