# Jan S. Hesthaven

#### Full Professor

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

**EPFL SB MATH MCSS **

MA C2 652 (Bâtiment MA)

Station 8

CH-1015 Lausanne

+41 21 693 03 51

+41 21 693 58 42

Office: MA C2 652

EPFL > SB > MATH > MCSS

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

### Biography

During the 3 years of study, the academic year of 1993-1994 was spend in the Division of Applied Mathematics at Brown University and three 3 months during the summer of 1994 in Department of Mathematics and Statistics at University of New Mexico. In August 1995, he recieved a Ph.D. in Numerical Analysis from the Institute of Mathematical Modelling (DTU).

Following graduation in August 1995, he was awarded an NSF Postdoctoral Fellowship in Advanced Scientific Computing and was approinted Visiting Assistant Professor in the Division of Applied Mathematics at Brown University. In December of 1996, he was appointed consultant to the Institute of Computer Applications in Science and Engineering(ICASE) at NASA Langley Research Center (NASA LaRC).

As of July 1999, he was appointed Assistant Professor of Applied Mathematics, in September 2000 he was awarded an Alfred P. Sloan Fellowship, as of July 2001 he was awarded a Manning Assistant Professorship, and in March 2002, he was awarded an NSF Career Award.

In January 2003, he was promoted to Associate Professor of Applied Mathematics with tenure and in May 2004 he was awarded Philip J. Bray Award for Excellence in Teaching in the Sciences (the highest award given for teaching excellence in all sciences at Brown University).

He was promoted to Professor of Applied Mathematics as of July 2005.

From October 2006 to June 2013, he was the Founding Director of the Center for Computation and Visualization (CCV) at Brown University.

As of October 2007, he holds the (honorary) title of Professor (Adjunct) at the Technical University of Denmark.

In November 2009, he successfully defended his dr.techn thesis at the Technical University of Denmark and was rewarded the degree of Doctor Technices -- the highest academic distinction awarded based on ... substantial and lasting contributions that has helped to move the research area forward and penetrated into applications.

As grant Co-PI he served from Aug 2010 to June 2013 as Deputy Director of the Institute of Computational and Experimental Research in Mathematics (ICERM), the newest NSF Mathematical Sciences Research Institute.

After having spend his entire academic career at Brown University, Prof Hesthaven decided to pursue new challenges and joined the Mathematics Institute of Computational Science and Engineering (MATHICSE) at Ecole Polytechnique Fédérale de Lausanne (EPFL) in Switzerland in July 2013.

In March 2014 he was elected SIAM Fellow for contributions to high-order methods for partial differential equations.

### Education

**Master of Science**

Computational Physics

Technical University of Denmark

01/91-08/91

**Doctor of Philosophy (PhD)**

Numerical analysis

Technical University of Denmark

08/92-08/95

**Doctor Technices (dr.techn)**

Computational Mathematics

Technical University of Denmark

11/2009

### Awards

**NSF Postdoctoral Fellowship**

US National Science Foundation

1995

**Alfred P. Sloan Research Fellowship**

Alfred P Sloan Foundation, US

2000

**Manning Assistant Professorship**

Brown University, US

2001

**NSF Career Award**

US National Science Foundation

2002

**Gutenberg Chair**

Gutenberg Foundation, France

2012

**Elected SIAM Fellow**

Society of Industrial and Applied Mathematics, US

2014

## Publications

### Infoscience publications

#### Journal Publications

# 2020

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

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

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

*Journal Of The Acoustical Society Of America*. 2020-11-01. DOI : 10.1121/10.0002448.

#### * A hierarchical preconditioner for wave problems in quasilinear complexity

2020-09-09.#### * Massive parallel nodal discontinuous Galerkin finite element method simulator for room acoustics

*International Journal of High Performance Computing Applications*. 2020-09-06.

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

*Advances in Computational Mathematics*. 2020-09-06. DOI : 10.1002/mma.5897.

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

*Journal Of Magnetic Resonance*. 2020-09-01. DOI : 10.1016/j.jmr.2020.106809.

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

*Computer Methods in Applied Mechanics and Engineering*. 2020-08-18. DOI : 10.1016/j.cma.2020.113315.

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

2020-07-23.#### * Hybrid high-resolution RBF-ENO method

*Journal of Computational Physics*. 2020-07-14.

#### * Rare event simulation for large-scale structures with local nonlinearities

*Computer Methods In Applied Mechanics And Engineering*. 2020-07-01. DOI : 10.1016/j.cma.2020.113051.

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

*Journal Of Scientific Computing*. 2020-06-03. DOI : 10.1007/s10915-020-01237-6.

#### * Constraint-aware neural networks for Riemann problems

*Journal Of Computational Physics*. 2020-05-15. DOI : 10.1016/j.jcp.2020.109345.

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

*Journal Of Computational Physics*. 2020-05-15. DOI : 10.1016/j.jcp.2020.109304.

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

*Computer Methods In Applied Mechanics And Engineering*. 2020-05-01. DOI : 10.1016/j.cma.2020.112896.

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

*Communications In Computational Physics*. 2020-05-01. DOI : 10.4208/cicp.OA-2019-0118.

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

2020-04-09.#### * Two-Dimensional RBF-ENO Method on Unstructured Grids

*Journal Of Scientific Computing*. 2020-03-11. DOI : 10.1007/s10915-020-01176-2.

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

*Journal Of Scientific Computing*. 2020-01-13. DOI : 10.1007/s10915-020-01123-1.

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

*Journal of Magnetic Resonance*. 2020.

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

*Journal of Computational Physics*. 2020. DOI : 10.1016/j.jcp.2020.109402.

# 2019

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

2019-12-23.#### * Modeling extended-reaction boundary conditions in time-domain wave-based simulations of room acoustics

2019-10-31.#### * Model order reduction for large-scale structures with local nonlinearities

*Computer Methods In Applied Mechanics and Engineering*. 2019-08-15. DOI : 10.1016/j.cma.2019.04.042.

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

*Ocean Modelling*. 2019-08-14. DOI : 10.1016/j.ocemod.2019.101429.

#### * Entropy Stable Essentially Nonoscillatory Methods Based On Rbf Reconstruction

*ESAIM: Mathematical Modelling and Numerical Analysis*. 2019-06-21. DOI : 10.1051/m2an/2019011.

#### * Time domain room acoustic simulations using the spectral element method

*Journal Of The Acoustical Society Of America*. 2019-06-01. DOI : 10.1121/1.5109396.

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

2019.#### * Estimation of groundwater storage from seismic data using deep learning

*Geophysics Research Letters*. 2019. DOI : 10.1111/1365-2478.12831.

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

*Journal of Computational Physics*. 2019. DOI : 10.1016/j.jcp.2019.03.050.

#### * Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems

*Journal of Scientific Computing*. 2019. DOI : 10.1007/s10915-018-0653-6.

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

*Computer Physics Communications*. 2019. DOI : 10.1016/j.cpc.2018.10.012.

# 2018

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

*Journal of Computational Physics*. 2018-11-01. DOI : 10.1016/j.jcp.2019.07.043.

#### * Data-driven reduced order modeling for time-dependent problems

*Computer Methods in Applied Mechanics and Engineering*. 2018-10. DOI : 10.1016/j.cma.2018.10.029.

#### * Entropy stable essentially non-oscillatory methods based on RBF reconstructions

*Mathematical Modeling and Numerical Analysis*. 2018-08-14.

#### * Conservative Model Order Reduction for Fluid Flow

*Advances in reduced order modeling*; Springer Verlag, 2018-08-06.

#### * Greedy Non-Intrusive Reduced Order Model for Fluid Dynamics

*AIAA Journal*. 2018-06-24. DOI : 10.2514/1.J056161.

#### * A data-driven shock capturing approach for discontinuous Galekin methods

2018-06-18.#### * Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem

*Journal of Computational Physics*. 2018-06-18. DOI : 10.1016/j.jcp.2019.01.031.

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

*Journal of Northwestern Polytechnical University*. 2018-06-01.

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

*Mathematics of computation*. 2018.

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

*Computational Geoscience*. 2018. DOI : 10.1007/s10596-019-9809-1.

#### * Symplectic Model-Reduction with a Weighted Inner Product

*SIAM Journal of Scientific Computing*. 2018.

#### * Flowfield Reconstruction Method Using Artificial Neural Network

*AIAA Journal*. 2018. DOI : 10.2514/1.J057108.

#### * Reduced order modeling for nonlinear structural analysis using Gaussian process regression

*Computer Methods in Applied Mechanics and Engineering*. 2018. DOI : 10.1016/j.cma.2018.07.017.

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

*Journal of Computational Physics*. 2018. DOI : 10.1016/j.jcp.2018.02.008.

#### * An artificial neural network as a troubled-cell indicator

*Journal of computational physics*. 2018. DOI : 10.1016/j.jcp.2018.04.029.

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

*Journal of Computational Physics*. 2018. DOI : 10.1016/j.jcp.2018.02.037.

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

*Journal of the Acoustical Society of America*. 2018. DOI : 10.1121/1.5024341.

#### * Research and Education in Computational Science and Engineering

*Siam Review*. 2018. DOI : 10.1137/16M1096840.

# 2017

#### * Numerical methods for conservation laws: From analysis to algorithms

Philadelphia: SIAM Publishing.#### * A comparative study of shock capturing models for the discontinuous Galerkin method

*Journal of Computational Physics*. 2017.

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

*Journal Of Scientific Computing*. 2017. DOI : 10.1007/s10915-016-0347-x.

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

*Journal of Computational Physics*. 2017. DOI : 10.1016/j.jcp.2018.04.056.

#### * A greedy non-intrusive reduced order model for fluid dynamics

*Journal of Northwestern Polytechnical University*. 2017.

#### * High-Order Accurate Local Schemes for Fractional Differential Equations

*Journal Of Scientific Computing*. 2017. DOI : 10.1007/s10915-015-0089-1.

#### * Identification of a Predator-Prey System from Simulation Data of a Convection Model

*Physics of Plasmas*. 2017. DOI : 10.1063/1.4977057.

#### * Efficient preconditioning of hp-FEM matrices arising from time-varying problems: an application to topology optimization

*Computer Methods in Applied Mechanics and Engineering*. 2017. DOI : 10.1016/j.cma.2017.04.027.

#### * Adaptive WENO methods based on radial basis functions reconstruction

*Journal of Scientific Computing*. 2017. DOI : 10.1007/s10915-017-0383-1.

#### * High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations

*Journal of Scientific Computing*. 2017. DOI : 10.1007/s10915-017-0393-z.

#### * Structure preserving model reduction of parametric Hamiltonian systems

*Siam Journal on Scientific Computing*. 2017. DOI : 10.1137/17M1111991.

#### * Space-dependent source determination in a time-fractional diffusion equation using a local discontinuous Galerkin method

*BIT Numerical Mathematics*. 2017. DOI : 10.1007/s10543-017-0648-y.

#### * A kernel compression scheme for fractional differential equations

*Siam Journal on Numerical Analysis*. 2017. DOI : 10.1137/15M1043960.

# 2016

#### * Spectral Methods for Hyperbolic Problems

*Handbook of Numerical Methods for Hyperbolic Problems Basic and Fundamental Issues*; Elsevier Publishing, 2016. p. 441-466.

#### * Spectral methods for tempered fractional differential equations

*Mathematics of Computation*. 2016.

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

*Journal of Scientific Computing*. 2016. DOI : 10.1007/s10915-016-0194-9.

# 2015

#### * Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Springer Verlag.#### * Hyperbolic Problems: Theory and Computation

*Journal Of Scientific Computing*. 2015. DOI : 10.1007/s10915-015-0065-9.

#### * An Adjoint Approach for Stabilizing the Parareal Method

*Comptes rendus des séances de l'Académie des Sciences. Série A, Sciences mathématiques***. 2015.

#### * Special Issue on "Fractional PDEs: Theory, Numerics, and Applications"

*Journal Of Computational Physics*. 2015. DOI : 10.1016/j.jcp.2015.04.007.

#### * Accuracy of high order and spectral methods for hyperbolic conservation laws with discontinuous solutions

*Siam Journal on Numerical Analysis*. 2015. DOI : 10.1137/140992758.

#### * Nodal discontinuous Galerkin methods for fractional diffusion equations on 2D domain with triangular meshes

*Journal of Computational Physics*. 2015. DOI : 10.1016/j.jcp.2015.06.022.

#### * Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

*Journal of Scientific Computing*. 2015. DOI : 10.1007/s10915-014-9959-1.

#### * A Parareal Method for Time-fractional Differential Equations

*Journal of Computational Physics*. 2015. DOI : 10.1016/j.jcp.2014.11.034.

#### * Local discontinuous Galerkin methods for fractional ordinary differential equations

*Bit Numerical Mathematics*. 2015. DOI : 10.1007/s10543-014-0531-z.

#### * Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method

*Communications in Computational Physics*. 2015. DOI : 10.4208/cicp.090314.151214a.

#### * Multilevel and Local Timestepping Discontinuous Galerkin Methods for Magma Dynamics

*Computational Geosciences*. 2015. DOI : 10.1007/s10596-015-9514-7.

#### * Reduced basis multiscale finite element methods for elliptic problems

*Multiscale Modeling and Simulation*. 2015. DOI : 10.1137/140955070.

#### * A Multi-domain Spectral Method for Time-fractional Differential Equations

*Journal of Computational Physics*. 2015. DOI : 10.1016/j.jcp.2014.10.016.

# 2014

#### * Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials

*Journal Of Computational Physics*. 2014. DOI : 10.1016/j.jcp.2013.11.018.

#### * Model Reduction Opportunities in Detailed Simulations of Combustion Dynamics

*Aiaa Journal*. 2014.

#### * Discontinuous Galerkin method for fractional convection-diffusion equations

*Siam Journal on Numerical Analysis*. 2014. DOI : 10.1137/130918174.

#### * High-order multiscale finite element method for elliptic problems

*Multiscale Modeling and Simulation*. 2014. DOI : 10.1137/120898024.

#### * Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods

*Mathematical Modelling and Numerical Analysis*. 2014. DOI : 10.1051/m2an/2013100.

#### * Multiscale modeling of sound propagation through the lung parenchyma

*Mathematical Modelling and Numerical Analysis*. 2014. DOI : 10.1051/m2an/2013093.

#### * Stable multi-domain spectral penalty methods for fractional partial differential equations

*Journal of Computational Physics*. 2014. DOI : 10.1016/j.jcp.2013.09.041.

#### * Fast prediction and evaluation of gravitational waveforms using surrogate models

*Physical Review X*. 2014. DOI : 10.1103/PhysRevX.4.031006.

# 2013

#### * High-order accurate methods for solving Maxwell's equations: Applications to photonic crystals and thin layer coatings

Saarbrucken, Germany: Scholar-Press.#### * On the use of reduced basis methods to accelerate and stabilize the Parareal method

*Reduced Order Methods for modeling and computational reduction*; Milano: Springer Publishing, 2013. p. 187-214.

#### * Local discontinuous Galerkin methods for fractional diffusion equations

*Mathematical Modelling and Numerical Analysis*. 2013. DOI : 10.1051/m2an/2013091.

#### * Multi-dimensional hybrid Fourier continuation-WENO solvers for conservation laws

*Journal of Computational Physics*. 2013. DOI : 10.1016/j.jcp.2013.07.009.

#### * A generalization of the Wiener rational basis functions on infinite intervals, Part II - Numerical investigation

*Journal of Computational and Applied Mathematics*. 2013. DOI : 10.1016/j.cam.2012.06.036.

# 2012

#### * High-Order Discontinuous Galerkin Methods by GPU Metaprogramming

*GPU Solutions to Multi-scale Problems in Science and Engineering*; Springer Verlag, 2012. p. 353-374.

#### * Special Issue in Memory of Professor David Gottlieb

France: SMAI Publications.#### * Solving Wave Equations on Unstructured Geometries

*GPU Computing Gems Jade Edition*; Morgan Kaufmann, 2012. p. 225-242.

#### * Accurate reconstruction of discontinuous functions using the singular pade-chebyshev method

*IAENG International Journal of Applied Mathematics*. 2012.

#### * Computation of connection coefficients and measure modifications for orthogonal polynomials

*BIT Numerical Mathematics*. 2012. DOI : 10.1007/s10543-011-0363-z.

#### * Certified Reduced Basis Method for the Electric Field Integral Equation

*SIAM Journal on Scientific Computing*. 2012. DOI : 10.1137/110848268.

#### * A reduced basis method for electromagnetic scattering by multiple particles in three dimensions

*Journal of Computational Physics*. 2012. DOI : 10.1016/j.jcp.2012.07.008.

#### * Certified reduced basis method for electromagnetic scattering and radar cross section estimation

*Computer Methods in Applied Mechanics and Engineering*. 2012. DOI : 10.1016/j.cma.2012.04.013.

### Teaching & PhD

#### Teaching

Mathematics