Related papers: An iterative multi-fidelity approach for model ord…

We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction-diffusion PDE (RD-PDE) systems. We show that solutions of…

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…

Subsampling of node sets is useful in contexts such as multilevel methods, computer graphics, and machine learning. On uniform grid-based node sets, the process of subsampling is simple. However, on node sets with high density variation,…

Aircraft design optimization traditionally relies on computationally expensive simulation techniques such as Finite Element Method (FEM) and Finite Volume Method (FVM), which, while accurate, can significantly slow down the design iteration…

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…

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

Stochastic reduced-order modeling based on time-dependent bases (TDBs) has proven successful for extracting and exploiting low-dimensional manifold from stochastic partial differential equations (SPDEs). The nominal computational cost of…

In this paper, we propose a network model, the multiclass classification-based reduced order model (MC-ROM), for solving time-dependent parametric partial differential equations (PPDEs). This work is inspired by the observation of applying…

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…

We target time-dependent partial differential equations (PDEs) with heterogeneous coefficients in space and time. To tackle these problems, we construct reduced basis/ multiscale ansatz functions defined in space that can be combined with…

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…

One of the major challenges in the Bayesian solution of inverse problems governed by partial differential equations (PDEs) is the computational cost of repeatedly evaluating numerical PDE models, as required by Markov chain Monte Carlo…

In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…

In many situations across computational science and engineering, multiple computational models are available that describe a system of interest. These different models have varying evaluation costs and varying fidelities. Typically, a…

Estimating probability of failure in aerospace systems is a critical requirement for flight certification and qualification. Failure probability estimation involves resolving tails of probability distribution, and Monte Carlo sampling…

Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…