相关论文: Exact Model Reduction by a Slow-Fast Decomposition…

The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…

Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by linear dynamics. For nonlinear dynamical systems exhibiting…

This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…

A fast convergence in a fixed-time of solutions of nonlinear dynamical systems, for which special requirements are satisfied on the derivative of a quadratic function calculated along the solutions of the system, is proposed. The conditions…

In this paper we study the dynamics of a fast-slow Fokker-Planck partial differential equation (PDE) viewed as the evolution equation for the density of a multiscale planar stochastic differential equation (SDE). Our key focus is on the…

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Understanding the quasi-static fracture formation and evolution is essential for assessing the mechanical properties and structural load-bearing capacity of materials. Peridynamics (PD) provides an effective computational method to depict…

Dynamic mode decomposition (DMD) and its variants have emerged as popular methods for the post-processing of fluid dynamics' simulations in order to visualize dominant coherent structures and to reduce the practical degrees of freedom to a…

In this paper implicit and explicit exact difference schemes (EDS) for system $\textbf{x}' = A\textbf{x}$ of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for…

We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensional fast-slow system is approximated well by the…

This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced…

Effective models for slender structures derived from well-known plate (or shell) theories are justified within the limit of a small thickness, and may therefore prove limited for intermediate slenderness. On the other hand, direct 3D…

We develop a family of stabilized backward differentiation formula (sBDF) schemes of orders one through four for semilinear parabolic equations. The proposed methods are designed to achieve three properties that are rarely available…

A systematic approach to nonlinear model order reduction (NMOR) of coupled fluid-structureflight dynamics systems of arbitrary fidelity is presented. The technique employs a Taylor series expansion of the nonlinear residual around…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Continuum soft robots are nonlinear mechanical systems with theoretically infinite degrees of freedom (DoFs) that exhibit complex behaviors. Achieving motor intelligence under dynamic conditions necessitates the development of…

Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…

We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…