相关论文: Interpolatory model reduction of dynamical systems…

The offline time of the reduced basis method can be very long given a large training set of parameter samples. This usually happens when the system has more than two independent parameters. On the other hand, if the training set includes…

This paper is concerned with the use of polynomial metamodels for the design of acoustical materials, considered as equivalent fluids. Polynomial series in microstructural parameters are considered, and allow us to approximate the…

Predicting and simulating aerodynamic fields for civil aircraft over wide flight envelopes represent a real challenge mainly due to significant numerical costs and complex flows. Surrogate models and reduced-order models help to estimate…

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

This paper describes novel algorithms for the identification of (almost-)resonant behavior in scattering problems. Our methods, relying on rational approximation, aim at building surrogate models of what we call "field amplification",…

Surrogate modeling is a viable solution for applications involving repetitive evaluations of expensive computational fluid dynamics models, such as uncertainty quantification and inverse problems. This study proposes a multi-layer…

This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the…

The central task in modeling complex dynamical systems is parameter estimation. This task involves numerous evaluations of a computationally expensive objective function. Surrogate-based optimization introduces a computationally efficient…

We consider a general nonlinear regression problem where the predictors contain measurement error. It has been recently discovered that several well-known dimension reduction methods, such as OLS, SIR and pHd, can be performed on the…

Multidisciplinary design optimization methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines. In this context, a large number of mixed continuous, integer and…

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…

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…

Stochastic inverse problems are generally solved by some form of finite sampling of a space of uncertain parameters. For computationally expensive models, surrogate response surfaces are often employed to increase the number of samples used…

High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…

Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based…

Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can…

High-fidelity models are essential for accurately capturing nonlinear system dynamics. However, simulation of these models is often computationally too expensive and, due to their complexity, they are not directly suitable for analysis,…

We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is…

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…