Related papers: Low-dimensional approximations of high-dimensional…

Here, we focus on Model Order Reduction (MOR) of non-parametric second-order dynamical systems. In these MOR algorithms, sequences of large and sparse linear systems arise during the model reduction process. Solving such linear systems is…

This work focuses on the space-time reduced-order modeling (ROM) method for solving large-scale uncertainty quantification (UQ) problems with multiple random coefficients. In contrast with the traditional space ROM approach, which performs…

In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…

Estimating parameters of Partial Differential Equations (PDEs) is of interest in a number of applications such as geophysical and medical imaging. Parameter estimation is commonly phrased as a PDE-constrained optimization problem that can…

We provide an introduction to POD-MOR with focus on (nonlinear) parametric PDEs and (nonlinear) time-dependent PDEs, and PDE constrained optimization with POD surrogate models as application. We cover the relation of POD and SVD, POD from…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…

In this paper, we present a reduced basis method for pricing European and American options based on the Black-Scholes and Heston model. To tackle each model numerically, we formulate the problem in terms of a time dependent variational…

The field of model order reduction (MOR) is growing in importance due to its ability to extract the key insights from complex simulations while discarding computationally burdensome and superfluous information. We provide an overview of MOR…

We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…

Stochastic differential equations have been an important tool in modeling complex financial relations, equipped with the possibility of being multidimensional to better oversee complexities inherent in finance. This multidimensionality,…

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…

Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…

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…

Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced…

A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

In recent years, the Adaptive Antoulas-Anderson AAA algorithm has established itself as the method of choice for solving rational approximation problems. Data-driven Model Order Reduction (MOR) of large-scale Linear Time-Invariant (LTI)…

A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-fidelity solutions is built by solving the parameterized…