Related papers: Multi-Region Matrix Interpolation for Dynamic Anal…
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…
The root mean squared error is an important measure used in a variety of applications such as structural dynamics and acoustics to model averaged deviations from standard behavior. For large-scale systems, simulations of this quantity…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
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…
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…
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…
Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…
Computational modeling of the structural behavior of continuous fiber composite materials often takes into account the periodicity of the underlying micro-structure. A well established method dealing with the structural behavior of periodic…
We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…
Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…
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…
Microstructure evolution, which plays a critical role in determining materials properties, is commonly simulated by the high-fidelity but computationally expensive phase-field method. To address this, we approximate microstructure evolution…
This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the…
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 present a novel derivative-free interpolation based optimization algorithm. A trust-region method is used where a surrogate model is realized via an interpolation framework. The framework for interpolation is provided by Universal…
Parameter estimation in structural dynamics generally involves inferring the values of physical, geometric, or even customized parameters based on first principles or expert knowledge, which is challenging for complex structural systems. In…
The last two decades have seen major developments in interpolatory methods for model reduction of large-scale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at modest cost; refined…
We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…
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…
In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay…