Related papers: Solving inverse scattering problems via reduced-or…
This paper proposes a data-driven algorithm for model order reduction (MOR) of large-scale wind farms and studies the effects that the obtained reduced-order model (ROM) has when this is integrated into the power grid. With respect to…
The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium. Deterministic methods can produce accurate solutions…
Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…
We propose KROM, a kernel-based reduced-order framework for fast solution of nonlinear partial differential equations. KROM formulates PDE solution as a minimum-norm (Gaussian-process) recovery problem in an RKHS, and accelerates the…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Partitioned methods allow one to build a simulation capability for coupled problems by reusing existing single-component codes. In so doing, partitioned methods can shorten code development and validation times for multiphysics and…
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…
Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…
We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a…
Reduced-order models (ROMs) of turbulent flows based on Galerkin projection often require many degrees of freedom to resolve the dynamics of the turbulence, or simulation data to obtain an optimal modal basis. However, obtaining simulation…
This paper formulates, analyzes, and demonstrates numerically a method for the partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order methods (FOMs). The…
Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…
We developed a novel reduced-order multi-scale method for solving large time-domain wavefield simulation problems. Our algorithm consists of two main stages. During the first "off-line" stage the fine-grid operator (of the graph Laplacian…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…
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…