相关论文: Efficient and certified solution of parametrized o…

This paper presents a projection-based reduced order modelling (ROM) framework for unsteady parametrized optimal control problems (OCP$_{(\mu)}$s) arising from cardiovascular (CV) applications. In real-life scenarios, accurately defining…

Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…

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,…

The numerical treatment of fluid-particle systems is a very challenging problem because of the complex coupling phenomena occurring between the two phases. Although accurate mathematical modelling is available to address this kind of…

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…

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) 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…

Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to…

A novel algorithmic discussion of the methodological and numerical differences of competing parametric model reduction techniques for nonlinear problems are presented. First, the Galerkin reduced basis (RB) formulation is presented which…

We present a framework that leverages the Discrete Empirical Interpolation Method (DEIM) for interpretable deep learning and dynamical system analysis. Although DEIM efficiently approximates nonlinear terms in projection-based reduced-order…

We propose a unified data-driven reduced order model (ROM) that bridges the performance gap between linear and nonlinear manifold approaches. Deep learning ROM (DL-ROM) using deep-convolutional autoencoders (DC-AE) has been shown to capture…

We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…

Motivated by the study of the electrodynamics of particles, we propose in this work an arbitrary-order discrete de Rham scheme for the treatment of elliptic problems with potential and flux jumps across a fixed interface. The scheme…

The onerous task of repeatedly resolving certain parametrized partial differential equations (pPDEs) in, e.g. the optimization context, makes it imperative to design vastly more efficient numerical solvers without sacrificing any accuracy.…

Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics.…

This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4,…

A genetic algorithm procedure is demonstrated that refines the selection of interpolation points of the discrete empirical interpolation method (DEIM) when used for constructing reduced order models for time dependent and/or parametrized…

Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…