Related papers: A Reduced Order Model for Finite Element Method in…

Time-dependent partial differential equations are ubiquitous in physics-based modeling, but they remain computationally intensive in many-query scenarios, such as real-time forecasting, optimal control, and uncertainty quantification.…

The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the…

The nuclear community has coupled several three-dimensional Computational Fluid Dynamics (CFD) solvers with one-dimensional system thermal-hydraulic (STH) codes. This work proposes to replace the CFD solver by a reduced order model (ROM) to…

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…

Objective: Inclusion of individualised electrical conductivities of head tissues is crucial for the accuracy of electrical source imaging techniques based on electro/magnetoencephalography and the efficacy of transcranial electrical…

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

An approach to derive low-complexity models describing thermal radiation for the sake of simulating the behavior of electric arcs in switchgear systems is presented. The idea is to approximate the (high dimensional) full-order equations,…

The timestep of the Finite-Difference Time-Domain method (FDTD) is constrained by the stability limit known as the Courant-Friedrichs-Lewy (CFL) condition. This limit can make FDTD simulations quite time consuming for structures containing…

Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate…

In part I of the article, we demonstrated that a variant of the Dynamic Mode Decomposition (DMD) algorithm based on variable projection optimization, called Optimized DMD (OPT-DMD), enables a robust identification of the dominant…

Frequency-based methods have been successfully employed in creating high fidelity data-driven reduced order models (DDROMs) for linear dynamical systems. These methods require access to values (and sometimes derivatives) of the…

Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

In this paper, we propose the Reduced Order Hysteretic Magnetization (ROHM) model to describe the magnetization and instantaneous power loss of composite superconductors subject to time-varying magnetic fields. Once the parameters of the…

We introduce a novel nonlinear imaging method for the acoustic wave equation based on data-driven model order reduction. The objective is to image the discontinuities of the acoustic velocity, a coefficient of the scalar wave equation from…

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…

POD--Galerkin reduced-order models (ROMs) for fluid-structure interaction problems (incompressible fluid and thin structure) are proposed in this paper. Both the high-fidelity and reduced-order methods are based on a Chorin-Temam…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

A multi-fidelity framework is established and demonstrated for prediction of combustion instabilities in rocket engines. The major idea is to adapt appropriate fidelity modeling approaches for different components in a rocket engine to…

The capacity to predict and control bioprocesses is perhaps one of the most important objectives of biotechnology. Computational simulation is an established methodology for the design and optimization of bioprocesses, where the finite…