Related papers: Reduced-order modeling for Ablowitz-Ladik equation

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient…

This paper presents a systematic methodology for the discretization and reduction of a class of one-dimensional Partial Differential Equations (PDEs) with inputs and outputs collocated at the spatial boundaries. The class of system that we…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Recent studies have demonstrated the great potential of reduced order modeling for parametric dynamical systems using low-rank tensor decompositions (LRTD). In particular, within the framework of interpolatory tensorial reduced order models…

This work presents a nonintrusive physics-preserving method to learn reduced-order models (ROMs) of Lagrangian systems, which includes nonlinear wave equations. Existing intrusive projection-based model reduction approaches construct…

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…

This paper presents an energy-preserving machine learning method for inferring reduced-order models (ROMs) by exploiting the multi-symplectic form of partial differential equations (PDEs). The vast majority of energy-preserving…

This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of…

Reduced order models (ROMs) are inexpensive surrogate models that reduce costs associated with many-query scenarios. Current methods for constructing entropy stable ROMs for nonlinear conservation laws utilize full order models (FOMs) based…

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. In this work, we develop data-driven reduced-order models (ROMs) for…

While reduced-order models (ROMs) have been popular for efficiently solving large systems of differential equations, the stability of reduced models over long-time integration is of present challenges. We present a greedy approach for ROM…

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

This study introduces a first step for constructing a hybrid reduced-order models (ROMs) for segregated fluid-structure interaction in an Arbitrary Lagrangian-Eulerian (ALE) approach at a high Reynolds number using the Finite Volume Method…

Projection-based model order reduction of an ordinary differential equation (ODE) results in a projected ODE. Based on this ODE, an existing reduced-order model (ROM) for finite volume discretizations satisfies the underlying conservation…

Reduced order modeling (ROM) is a field of techniques that approximates complex physics-based models of real-world processes by inexpensive surrogates that capture important dynamical characteristics with a smaller number of degrees of…