相关论文: Parametric Reduced Order Models for the Generalize…

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…

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…

Even with the most advanced computational capabilities, high-fidelity (e.g., large-eddy) simulations of large-scale rocket engines remain far out of reach. In the current work, we develop and establish a component-based reduced-order…

This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available:…

In this work, a novel method with an adaptive functional basis for reduced order models (ROM) based on proper orthogonal decomposition (POD) is introduced. The method is intended to be applied in particular to hydrocarbon reservoir…

In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of…

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

In this paper, we investigate the modeling of sub-scale components of proper orthogonal decomposition reduced order models (POD-ROMs) of convection-dominated flows. We propose ROM closure models that depend on the ROM residual. We…

This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Galerkin and Petrov-Galerkin projection-based reduced-order models (ROMs) of transient partial differential equations are typically obtained by performing a dimension reduction and projection process that is defined at either the spatially…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

It is argued that the two problems of choosing characterizations and models of complex systems should not be considered independently. A particular criterion for these choices, oriented on the potential usefulness of the results, is…

We propose a new method in which a generative network (GN) integrate into a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and…

We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the…

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 work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…