Related papers: Coarse-Proxy Reduced Basis Methods for Integral Eq…
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…
A subspace method is introduced to solve large-scale trace ratio problems. This approach is matrix-free, requiring only the action of the two matrices involved in the trace ratio. At each iteration, a smaller trace ratio problem is…
Inverse imaging problems rely on limited and indirect measurements, making reconstruction highly dependent on both regularization and sample locations. We introduce a novel greedy framework for the optimal selection of indirect measurements…
We present a new rational approximation algorithm based on the empirical interpolation method for interpolating a family of parametrized functions to rational polynomials with invariant poles, leading to efficient numerical algorithms for…
We develop likelihood-based bias reduction for nonlinear panel models with additive individual and time effects. In two-way panels, integrated-likelihood corrections are attractive but challenging because the required integration is high…
Scale analysis based on coarse-graining has been proposed recently as an alternative to Fourier analysis. It is now broadly used to analyze energy spectra and energy transfers in eddy-resolving ocean simulations. However, for data from…
We introduce a hyperreduced reduced basis element method for model reduction of parameterized, component-based systems in continuum mechanics governed by nonlinear partial differential equations. In the offline phase, the method constructs,…
We propose a certified reduced basis approach for the strong- and weak-constraint four-dimensional variational (4D-Var) data assimilation problem for a parametrized PDE model. While the standard strong-constraint 4D-Var approach uses the…
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount of input data vectors,…
This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modelling. Building upon the success of…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
Robust light transport algorithms, particularly bidirectional path tracing (BDPT), face significant challenges when dealing with specular or highly glossy involved paths. BDPT constructs the full path by connecting sub-paths traced…
We address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid-structure interaction or shape optimization problems. In this paper, we focus…
In this paper we discuss a projection model order reduction (MOR) method for a class of parametric linear evolution PDEs, which is based on the application of the Laplace transform. The main advantage of this approach consists in the fact…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
The Reduced Basis (RB) method is a well established method for the model order reduction of problems formulated as parametrized partial differential equations. One crucial requirement for the application of RB schemes is the availability of…