Related papers: A reduced-order model for advection-dominated prob…

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…

This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…

We continue to study the problem of modeling of substitution of production factors motivated by the need for computable mathematical models of economics that could be used as a basis in applied developments. This problem has been studied…

Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…

A data-driven, model-free framework is introduced for calculating Reduced-Order Models (ROMs) capable of accurately predicting time-mean responses to external forcings, or forcings needed for specified responses, e.g., for control, in fully…

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

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…

A major goal for reduced-order models of unsteady fluid flows is to uncover and exploit latent low-dimensional structure. Proper orthogonal decomposition (POD) provides an energy-optimal linear basis to represent the flow kinematics, but…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…

Linear block transform coding remains a fundamental component of image and video compression. Although the Discrete Cosine Transform (DCT) is widely employed in all current compression standards, its sub-optimality has sparked ongoing…

The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…

Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…