Jan Sickmann Hesthaven

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We propose a simulation-based decision strategy for the proactive maintenance of complex structures with a particular application to structural health monitoring (SHM). The strategy is based on a data-driven approach which exploits an offline-online decomp ...

Projection-based reduced order models (ROM) based on the weak form and the strong form of the discontinuous Galerkin (DG) method are proposed and compared for shock-dominated problems. The incorporation of dissipation components of DG in a consistent manne ...

Highly accurate numerical or physical experiments are often very time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the amount of available samples may be too limited to provide satisfactory ...

This paper presents an equivalent fluid model (EFM) formulation in a three-dimensional time-domain discontinuous Galerkin finite element method framework for room acoustic simulations. Using the EFM allows for the modeling of the extended-reaction (ER) beh ...

High-order numerical solvers for conservation laws suffer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amoun ...

When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for parametrized, time-dependent problems in engineering computations, it is often t ...

Numerical simulation of parametrized differential equations is of crucial importance in the study of real-world phenomena in applied science and engineering. Computational methods for real-time and many-query simulation of such problems often require prohi ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life ...

Hyperbolic conservation laws play a critical role in various fields, including aerodynamics, physics, and oceanography. However, traditional physics-informed neural networks (PINNs), despite their remarkable capabilities in solving partial differential equ ...

The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torre ...

We investigate reduced order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the construction of a reduc ...

A data-driven reduced basis (RB) method for parametrized time-dependent problems is proposed. This method requires the offline preparation of a database comprising the time history of the full-order solutions at parameter locations. Based on the full-order ...

The nonlocal nature of the fractional integral makes the numerical treatment of fractional dierential equations expensive in terms of computational eort and memory requirements. In this paper we propose a method to reduce these costs while controlling the ...

Optimum groundwater management is important for addressing the global challenges of water scarcity, especially in arid regions. This study demonstrates the application of synthetic data combined with seismic methods to quantify water volumes in a controlle ...

We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...

In environmental acoustics and in room acoustics, many surfaces exhibit extended-reaction (ER) behavior, i.e., their surface impedance varies with the angle of the incident sound wave. This paper presents a phenomenological method for modeling such angle d ...

. High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on a set of para ...

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold struc ...

We propose two different improvements of reduced basis (RB) methods to enable the efficient and accurate evaluation of an output functional based on the numerical solution of parametrized partial differential equations with a possibly high-dimensional para ...

Jan Sickmann Hesthaven

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Simulation-based Anomaly Detection and Damage Localization: An application to Structural Health Monitoring

Model order reduction for compressible flows solved using the discontinuous Galerkin methods

Multi-fidelity regression using artificial neural networks: Efficient approximation of parameter-dependent output quantities

Time-domain room acoustic simulations with extended-reacting porous absorbers using the discontinuous Galerkin method

Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial viscosity tuned by neural networks

Multi-fidelity surrogate modeling using long short-term memory networks

Reduced basis methods for time-dependent problems

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Model order reduction for large-scale structures with local nonlinearities

A coordinate transformation-based physics-informed neural networks for hyperbolic conservation laws

Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domains

Galerkin neural network-POD for acoustic and electromagnetic wave propagation in parametric domains

Data-driven reduced order modeling for time-dependent problems

A kernel compression scheme for fractional differential equations

Uncertainty quantification in groundwater volume predictions from seismic data using neural networks

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

A phenomenological extended-reaction boundary model for time-domain wave-based acoustic simulations under sparse reflection conditions using a wave splitting method

Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation

Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure

On the use of ANOVA expansions in reduced basis methods for high-dimensional parametric partial differential equations