Related papers: Block Structure Preserving Model Order Reduction f…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…
In this note we discuss the construction of high order asymptotic preserving numerical schemes for the Boltzmann equation. The methods are based on the use of Implicit-Explicit (IMEX) Runge-Kutta methods combined with a penalization…
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…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…
The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
In order to achieve a better understanding of degradation processes in lithium-ion batteries, the modelling of cell dynamics at the mircometer scale is an important focus of current mathematical research. These models lead to…
Accurate electrochemical models are essential for the safe and efficient operation of lithium-ion batteries in real-world applications such as electrified vehicles and grid storage. Reduced-order models (ROM) offer a balance between…
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…
Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…
In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. The proposed PDE has the form of continuity equation that arises in various research areas, e.g. fluid dynamics and…
This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…