Related papers: Basic Ideas and Tools for Projection-Based Model R…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
We present a model reduction approach that extends the original empirical interpolation method to enable accurate and efficient reduced basis approximation of parametrized nonlinear partial differential equations (PDEs). In the presence of…
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…
Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…
We present an introduction to some of the state of the art in reduced order and surrogate modeling in gravitational wave (GW) science. Approaches that we cover include Principal Component Analysis, Proper Orthogonal Decomposition, the…
Interpolatory projection methods for model reduction of nonparametric linear dynamical systems have been successfully extended to nonparametric bilinear dynamical systems. However, this is not the case for parametric bilinear systems. In…
We propose a model reduction technique for parametrized partial differential equations arising from scalar hyperbolic conservation laws. The key idea of the technique is to construct basis functions that are local in parameter and time…
We propose a method to reduce the computational effort to solve a partial differential equation on a given domain. The main idea is to split the domain of interest in two subdomains, and to use different approximation methods in each of the…
Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly…
We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…
This paper considers the creation of parametric surrogate models for applications in science and engineering where the goal is to predict high-dimensional spatiotemporal output quantities of interest, such as pressure, temperature and…
This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…
We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected…
Discrete empirical interpolation method (DEIM) is a popular technique for nonlinear model reduction and it has two main ingredients: an interpolating basis that is computed from a collection of snapshots of the solution and a set of indices…
In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with affine parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its…