Related papers: Model Order Reduction by Proper Orthogonal Decompo…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…
This study explores reduced-order modeling for analyzing the time-dependent diffusion-deformation of hydrogels. The full-order model describing hydrogel transient behavior consists of a coupled system of partial differential equations in…
Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…
In recent decades, the main focus of computer modeling has been on supporting the design and development of engineering prototyes, but it is now ubiquitous in non-traditional areas such as medical rehabilitation. Conventional modeling…
The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to…
Dimension reduction is a fundamental tool for analyzing high-dimensional data in supervised learning. Traditional methods for estimating intrinsic order often prioritize model-specific structural assumptions over predictive utility. This…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter…
In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…
This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…
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…
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied…
We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Theory and methods to obtain parametric reduced-order models by moment matching are presented. The definition of the parametric moment is introduced, and methods (model-based and data-driven) for the approximation of the parametric moment…
In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
A space-time-parameters structure of parametric parabolic PDEs motivates the application of tensor methods to define reduced order models (ROMs). Within a tensor-based ROM framework, the matrix SVD - a traditional dimension reduction…
Echo State Networks (ESN) are a type of Recurrent Neural Network that yields promising results in representing time series and nonlinear dynamic systems. Although they are equipped with a very efficient training procedure, Reservoir…