Related papers: Model Reduction for Multi-Scale Transport Problems…
We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which which suggests…
This work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov-)Galerkin…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations.…
Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of certain partial differential equations (PDEs) using conventional techniques…
A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method,…
We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
Recently, a Levenberg-Marquardt method with Singular Scaling matrix, called LMMSS, was proposed and successfully applied in parameter estimation in heat conduction problems, where the choice of suitable singular scaling matrix resulted in…
Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral methods). Thus,…
Recently, collocation based radial basis function (RBF) partition of unity methods (PUM) for solving partial differential equations have been formulated and investigated numerically and theoretically. When combined with stable evaluation…
Deep Learning Reduced Order Models (ROMs) are becoming increasingly popular as surrogate models for parametric partial differential equations (PDEs) due to their ability to handle high-dimensional data, approximate highly nonlinear…
This paper formulates, analyzes, and demonstrates numerically a method for the partitioned solution of coupled interface problems involving combinations of projection-based reduced order models (ROM) and/or full order methods (FOMs). The…
Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity…
The Kolmogorov $n$-width of the solution manifolds of transport-dominated problems can decay slowly. As a result, it can be challenging to design efficient and accurate reduced order models (ROMs) for such problems. To address this issue,…