Related papers: A method for nonlinear modal analysis and synthesi…
Reduced-order models (ROMs) that capture changes in fluid systems due to variations in parameters, such as the Reynolds number or the shape of a stationary body placed in the flow, are attracting increasing attention in engineering…
In this study, we present a non-intrusive reduced order modeling (ROM) framework for large-scale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM)…
The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…
We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…
High-fidelity simulation of nonequilibrium plasmas -- crucial to applications in electric propulsion, hypersonic re-entry, and astrophysical flows -- requires state-specific collisional-radiative (CR) kinetic models, but these come at a…
We propose a regularization for Reduced Order Models (ROMs) of the quasi-geostrophic equations (QGE) to increase accuracy when the Proper Orthogonal Decomposition (POD) modes retained to construct the reduced basis are insufficient to…
Model reduction by projection-based approaches is often associated with losing some of the important features that contribute towards the dynamics of the retained scales. As a result, a mismatch occurs between the predicted trajectories of…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
The Allen-Cahn equation is a gradient system, where the free-energy functional decreases monotonically in time. We develop an energy stable reduced order model (ROM) for a gradient system, which inherits the energy decreasing property of…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system.…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…
The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate…
This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…
In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…
Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous…
The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…