Deep ReLU networks and high-order finite element methods
Approximation rate bounds for emulations of real-valued functions on intervals by deep
neural networks (DNNs) are established. The approximation results are given for DNNs …
neural networks (DNNs) are established. The approximation results are given for DNNs …
Component-wise reduced order model lattice-type structure design
S McBane, Y Choi - Computer methods in applied mechanics and …, 2021 - Elsevier
Lattice-type structures can provide a combination of stiffness with light weight that is
desirable in a variety of applications. Design optimization of these structures must rely on …
desirable in a variety of applications. Design optimization of these structures must rely on …
Domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) nonlinear model reduction
A novel domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) model-reduction
method applicable to parameterized systems of nonlinear algebraic equations (eg, arising …
method applicable to parameterized systems of nonlinear algebraic equations (eg, arising …
Localized model reduction for nonlinear elliptic partial differential equations: localized training, partition of unity, and adaptive enrichment
We propose a component-based (CB) parametric model order reduction (pMOR) formulation
for parameterized nonlinear elliptic partial differential equations. CB-pMOR is designed to …
for parameterized nonlinear elliptic partial differential equations. CB-pMOR is designed to …
A non-overlapping optimization-based domain decomposition approach to component-based model reduction of incompressible flows
We present a component-based model order reduction procedure to efficiently and
accurately solve parameterized incompressible flows governed by the Navier-Stokes …
accurately solve parameterized incompressible flows governed by the Navier-Stokes …
Randomized local model order reduction
In this paper we propose local approximation spaces for localized model order reduction
procedures such as domain decomposition and multiscale methods. Those spaces are …
procedures such as domain decomposition and multiscale methods. Those spaces are …
A non-conforming dual approach for adaptive trust-region reduced basis approximation of PDE-constrained parameter optimization
In this contribution we propose and rigorously analyze new variants of adaptive Trust-
Region methods for parameter optimization with PDE constraints and bilateral parameter …
Region methods for parameter optimization with PDE constraints and bilateral parameter …
[PDF][PDF] Localized model reduction for parameterized problems
In this contribution we present a survey of concepts in localized model order reduction
methods for parameterized partial differential equations. The key concept of localized model …
methods for parameterized partial differential equations. The key concept of localized model …
A reduced basis super-localized orthogonal decomposition for reaction-convection-diffusion problems
This paper presents a method for the numerical treatment of reaction-convection-diffusion
problems with parameter-dependent coefficients that are arbitrary rough and possibly …
problems with parameter-dependent coefficients that are arbitrary rough and possibly …
Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based …
K Mitra, M Vohralík - 2023 - inria.hal.science
We consider numerical approximations of nonlinear, monotone, and Lipschitz-continuous
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …
elliptic problems, with gradient-dependent or gradient-independent diffusivity. For this …