Related papers: Exact Model Reduction by a Slow-Fast Decomposition…
Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed by Galerkin projection of the governing equations onto a…
In this paper, we propose a general sparse decomposition of dynamical systems provided that the vector field and constraint set possess certain sparse structures, which we call subsystems. This notion is based on causal dependence in the…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
The decay of a general time dependent structure factors is considered. The dynamics is that of stochastic field equations of the Langevin type, where the systematic generalized force is a functional derivative of some classical field…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…
This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…
We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…
Chemical reactions modeled by ordinary differential equations are finite-dimensional dissipative dynamical systems with multiple time-scales. They are numerically hard to tackle -- especially when they enter an optimal control problem as…
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,…
We consider finite-dimensional many-body quantum systems described by time-independent Hamiltonians and Markovian master equations, and present a systematic method for constructing smaller-dimensional, reduced models that exactly reproduce…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by…
The availability of precise and accurate simulation is a limiting factor for interpreting and forecasting data in many fields of science and engineering. Often, one or more distinct simulation software applications are developed, each with…
Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…
A novel dynamic mode decomposition (DMD) method based on a Kalman filter is proposed. This paper explains the fast algorithm of the proposed Kalman filter DMD (KFDMD) in combination with truncated proper orthogonal decomposition for…
We apply the proper orthogonal decomposition (POD) to the nonlinear Schr\"odinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving…
In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…
Inverse design of slender elastic structures underlies a wide range of applications in computer graphics, flexible electronics, biomedical devices, and soft robotics. Traditional optimization-based approaches, however, are often orders of…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…