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In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a…

This work deals with tailored reduced order models for bifurcating nonlinear parametric partial differential equations, where multiple coexisting solutions arise for a given parametric instance. Approaches based on proper orthogonal…

This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…

We present an algorithm to generate application-specific, global reduced order quadratures (ROQ) for multiple fast evaluations of weighted inner products between parameterized functions. If a reduced basis (RB) or any other projection-based…

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

The task of repeatedly solving parametrized partial differential equations (pPDEs) in, e.g. optimization or interactive applications, makes it imperative to design highly efficient and equally accurate surrogate models. The reduced basis…

Gas transport and other complex real-world challenges often require solving and controlling partial differential equations (PDEs) defined on graph structures, which typically demand substantial memory and computational resources. The Random…

We present an accelerated greedy strategy for training of projection-based reduced-order models for parametric steady and unsteady partial differential equations. Our approach exploits hierarchical approximate proper orthogonal…

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.…

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…

We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…

We introduce hp-greedy, a refinement approach for building gravitational wave surrogates as an extension of the standard reduced basis framework. Our proposal is data-driven, with a domain decomposition of the parameter space, local reduced…

Dimension reduction is often needed in the area of data mining. The goal of these methods is to map the given high-dimensional data into a low-dimensional space preserving certain properties of the initial data. There are two kinds of…

Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they have been used, largely in nuclear physics, as fast emulators able to bypass expensive direct computations while still providing…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

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…