Jan S. Hesthaven

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Vice-président académique

jan.hesthaven@epfl.ch +41 21 693 03 51 https://www.epfl.ch/labs/mcss/

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https://orcid.org/0000-0001-8074-1586

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+41 21 693 03 51
EPFL > VPA > VPA-VP > VPA-VP-GE

EPFL SB MATH MCSS
MA C2 652 (Bâtiment MA)
Station 8
CH-1015 Lausanne

+41 21 693 03 51
+41 21 693 58 42
Local: MA C2 652
EPFL > SB > MATH > MCSS

Web site: Site web: https://mcss.epfl.ch/

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Domaines de compétences

The research activities focuses on the development, analysis and application of high-order accurate computational methods for time-dependent partial differential equations with a particular emphasis on linear and nonlinear wave problems. This has and continues to included research activities in discontinuous Galerkin and spectral methods, certificed reduced basis methods, methods for uncertainty quantification, methods for multiscale problems in time and space, efficient multilevel solvers and fractional differential equations. A major recent activity is the use of machine learning techniques in computational science with an emphasis on methods that preserve physical characteristics or the use of local neural networks to accelerate existing methods rather than replacing them.

While the emphasis in on the development and analysis of new methods and algorithms, the research is application driven and we generally maintain a strong focus on tying the theoretical developments to real applications, ranging from electromagnetics and plasma physics to geoscience and combustion. There is also a sustained interest in the development of methods and algorithms for parallel computing, GPU accelerated computing and the development of resilient algorithms, to support the development and use of large scale computational tool to enable predictive similation science.

Publications

Publications Infoscience

Jan S Hesthaven publications

2020

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

L. Zhao; W. Deng; J. S. Hesthaven

Science China-Mathematics. 2020-11-18. DOI : 10.1007/s11425-019-1720-1.

Jan S. Hesthaven

Vice-président académique

Domaines de compétences

Publications

Publications Infoscience

Jan S Hesthaven publications

2020

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

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

Controlling oscillations in spectral schemes using Artificial Neural Networks

A hierarchical preconditioner for wave problems in quasilinear complexity

Massive parallel nodal discontinuous Galerkin finite element method simulator for room acoustics

Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation

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

Systematic sensor placement for structural anomaly detection in the absence of damaged states

Physics-informed machine learning for reduced-order modeling of nonlinear problems

Hybrid high-resolution RBF-ENO method

Rare event simulation for large-scale structures with local nonlinearities

An edge detector based on artificial neural network with application to hybrid Compact-WENO finite difference schemes

A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

Constraint-aware neural networks for Riemann problems

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

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

A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework

Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks

Two-Dimensional RBF-ENO Method on Unstructured Grids

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Numerical methods for structural anomaly detection using model order reduction and data-driven techniques

High-order essentially nonoscillatory methods based on radial basis functions

Effective diffusion tensor measured by diffusion MRI of moving and deforming domains

Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism

2019

Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method

Modeling extended-reaction boundary conditions in time-domain wave-based simulations of room acoustics

Model order reduction for large-scale structures with local nonlinearities

A comparative study of earthquake source models in high- order accurate tsunami simulations

Entropy Stable Essentially Nonoscillatory Methods Based On Rbf Reconstruction

Time domain room acoustic simulations using the spectral element method

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

MATHICSE Technical Report: Time domain room acoustic simulations using a spectral element method

MATHICSE Technical Report: Simulation-Based Anomaly Detection and Damage Localization: an Application to Structural Health Monitoring

MATHICSE Technical Report: A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism

Entropy stable essentially non-oscillatory methods based on RBF reconstructions

Estimation of groundwater storage from seismic data using deep learning

Discontinuous Galerkin Discretizations of the Boltzmann Equations in 2D: semi-analytic time stepping and absorbing boundary layers

Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

Projective multiscale time-integration for electrostatic particle-in-cell methods

2018

RBF Based CWENO Method

Detecting troubled-cells on two-dimensional unstructured grids using a neural network

Data-driven reduced order modeling for time-dependent problems

Conservative Model Order Reduction for Fluid Flow

Greedy Non-Intrusive Reduced Order Model for Fluid Dynamics

A data-driven shock capturing approach for discontinuous Galekin methods

Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

POD-Kriging reduced method’s application in Tandem Cylinders’ flow

Controlling oscillations in high-order schemes using neural networks

Scaling and Resilience in Numerical Algorithms for Exascale Computing

Geometric Model Order Reduction

Fast hierarchical solvers for symmetric eigenvalue problems

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

A nodal discontinuous Galerkin finite element method for the poroelastic wave equation

Multi space reduced basis preconditioners for parametrized partial differential equations

Symplectic Model-Reduction with a Weighted Inner Product

Flowfield Reconstruction Method Using Artificial Neural Network

Reduced order modeling for nonlinear structural analysis using Gaussian process regression

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

An artificial neural network as a troubled-cell indicator

Non-intrusive reduced order modeling of nonlinear problems using neural networks

Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography

Research and Education in Computational Science and Engineering

2017

Numerical methods for conservation laws: From analysis to algorithms

A comparative study of shock capturing models for the discontinuous Galerkin method

Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations

Dynamical Low Rank approximation of PDEs with random parameters

Large-Scale Tsunami Simulations using the Discontinuous Galerkin Method

Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial dierential equations