Publications de Jan Sickmann Hesthaven

Leveraging Contrast Agent Kinetics for Robust Reflectance Mode Fluorescence Tomography

Fluorescence Image Guided Surgery utilizes continuous wave epi-fluorescence measurements on the tissue surface to locate targets such as tumors or lymph nodes, but precise 3D localization of deep targets remains intractable due to the illposedness of the a ...

IEEE2025

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

Jan Sickmann Hesthaven, Mariella Kast

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 ...

2025

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

Jan Sickmann Hesthaven

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 ...

2025

Perfectly matched layers for the Boltzmann equation: Stability and sensitivity analysis

Jan Sickmann Hesthaven

We study the stability and sensitivity of an absorbing layer for the Boltzmann equation by examining the Bhatnagar-Gross-Krook (BGK) approximation and using the perfectly matched layer (PML) technique. To ensure stability, we discard some parameters in the ...

Academic Press Inc Elsevier Science2024

Machine-Learning-Enhanced Real-Time Aerodynamic Forces Prediction Based on Sparse Pressure Sensor Inputs

Jan Sickmann Hesthaven, Junming Duan

Accurate real-time prediction of aerodynamic forces is crucial for the navigation of unmanned aerial vehicles (UAVs). This paper presents a data-driven aerodynamic force prediction model based on a small number of pressure sensors located on the surface of ...

2024

Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks

Jan Sickmann Hesthaven, Mariella Kast

This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time -dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of the ...

2024

GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications

Jan Sickmann Hesthaven, Federico Pichi

This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the concept of feed ...

2024

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

Jan Sickmann Hesthaven

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 ...

European Association of Geoscientists and Engineers, EAGE2024

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

Jan Sickmann Hesthaven, Federico Pichi

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 ...

Academic Press Inc Elsevier Science2024

A Fast Direct Solver for Higher Order Discretizations of Integral Equations

Jan Sickmann Hesthaven

This paper presents a fast direct solver for the Combined Field Integral Equation using higher-order discretizations. By adopting higher-order polynomials with the Method of Moments, the number of unknowns is significantly reduced. The fast direct solver l ...

Institute of Electrical and Electronics Engineers Inc.2024

Monitoring of water volume in a porous reservoir using seismic data: A 3D simulation study

Jan Sickmann Hesthaven

A potential framework to estimate the volume of water stored in a porous storage reservoir from seismic data is neural networks. In this study, the man-made groundwater reservoir is modeled as a coupled poroviscoelastic–viscoelastic medium, and the underly ...

2024

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Elsevier Science Sa2024

A new variable shape parameter strategy for RBF approximation using neural networks

Jan Sickmann Hesthaven

The choice of the shape parameter highly effects the behaviour of radial basis function (RBF) approximations, as it needs to be selected to balance between the ill-conditioning of the interpolation matrix and high accuracy. In this paper, we demonstrate ho ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Monitoring of water table level and volume of water in a porous storage by seismic data

Jan Sickmann Hesthaven

Neural networks provide an attractive framework to monitor the water table level and the volume of stored water in porous media from seismic data in an automated, fast and cost-efficient manner. In this work, a subsurface reservoir is modeled as a coupled ...

European Association of Geoscientists and Engineers, EAGE2023

An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

Jan Sickmann Hesthaven, Federico Pichi

This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we ...

PERGAMON-ELSEVIER SCIENCE LTD2023

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Jan Sickmann Hesthaven, Junming Duan

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

Academic Press Inc Elsevier Science2023

Localized model order reduction and domain decomposition methods for coupled heterogeneous systems

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a model order reduction technique to accurately approximate the behavior of multi-component systems without any a-priori knowledge of the coupled model. In the offline phase, we construct independent surrogate models by solving the local problem ...

Wiley2023

Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics

Jan Sickmann Hesthaven

We present a massively parallel and scalable nodal discontinuous Galerkin finite element method (DGFEM) solver for the time-domain linearized acoustic wave equations. The solver is implemented using the libParanumal finite element framework with extensions ...

Sage Publications Ltd2023

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

Cecilia Pagliantini, Jan Sickmann Hesthaven, Nicolò Ripamonti

. 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 ...

AMER MATHEMATICAL SOC2023

Rank-adaptive structure-preserving model order reduction of Hamiltonian systems

Cecilia Pagliantini, Jan Sickmann Hesthaven, Nicolò Ripamonti

This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To overcome the slowly decaying Kolmogorov width typical of transport problems, the ...

EDP SCIENCES S A2022