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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,…

Simulation models are widely used in practice to facilitate decision-making in a complex, dynamic and stochastic environment. But they are computationally expensive to execute and optimize, due to lack of analytical tractability. Simulation…

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…

Not being able to understand and predict the behavior of deep learning systems makes it hard to decide what architecture and algorithm to use for a given problem. In science and engineering, modeling is a methodology used to understand…

This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the…

In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…

While the prediction of AC losses during transients is critical for designing large-scale low-temperature superconducting (LTS) magnets, brute-force finite-element (FE) simulation of their detailed geometry down to the length scale of the…

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…

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…

Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of…

Concurrent multiscale finite element analysis (FE2) is a powerful approach for high-fidelity modeling of materials for which a suitable macroscopic constitutive model is not available. However, the extreme computational effort associated…

The finite element method (FEM) is commonly used in computational cardiac simulations. For this method, a mesh is constructed to represent the geometry and, subsequently, to approximate the solution. To accurately capture curved geometrical…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…

During the design process of an autonomous underwater vehicle (AUV), the pressure vessel has a critical role. The pressure vessel contains dry electronics, power sources, and other sensors that can not be flooded. A traditional design…

For many novel applications, such as patient-specific computer-aided surgery, conventional solution techniques of the underlying nonlinear problems are usually computationally too expensive and are lacking information about how certain can…

Machine learning models of accelerator systems (`surrogate models') are able to provide fast, accurate predictions of accelerator physics phenomena. However, approaches to date typically do not include measured input diagnostics, such as…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

The term `surrogate modeling' in computational science and engineering refers to the development of computationally efficient approximations for expensive simulations, such as those arising from numerical solution of partial differential…

This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…