Jan S. Hesthaven
Expertise
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.
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.
Expertise
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.
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.
Prof. Hesthaven received an M.Sc. in computational physics from the Technical University of Denmark (DTU) in August 1991. During the studies, the last 6 months of 1989 was spend at JET, the european fusion laboratory in Culham, UK. Following graduation, he was awarded a 3 year fellowship to begin work towards a Ph.D. at Riso National Laboratory in the Department of Optics and Fluid Dynamics.
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.
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
Doctor Technices (dr.techn)
| Computational Mathematics2009 – 2009 Technical University of Denmark
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
SIAM Fellow
Society of Industrial and Applied Mathematics, US
2014
NSF Career Award
US National Science Foundation
2002
AMS Fellow
American Mathematical Society
2022
Fellow (Foreign)
Royal Danish Academy of Sciences and Letters
2022
Jan S Hesthaven publications
2025
Neural Empirical Interpolation Method for Nonlinear Model Reduction
SIAM Journal on Scientific Computing. 2025. DOI : 10.1137/24m1681434.A coordinate transformation-based physics-informed neural networks for hyperbolic conservation laws
Journal of Computational Physics. 2025. DOI : 10.1016/j.jcp.2025.114161.Galerkin neural network-POD for acoustic and electromagnetic wave propagation in parametric domains
Advances in Computational Mathematics. 2025. DOI : 10.1007/s10444-025-10245-9.Leveraging Contrast Agent Kinetics for Robust Reflectance Mode Fluorescence Tomography
2025. 2025 IEEE 22nd International Symposium on Biomedical Imaging (ISBI), Houston, TX, USA, 2025-04-14 - 2025-04-17. DOI : 10.1109/isbi60581.2025.10980828.2024
GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications
Computer Methods in Applied Mechanics and Engineering. 2024. DOI : 10.1016/j.cma.2024.117458.Monitoring of water volume in a porous reservoir using seismic data: A 3D simulation study
Journal of Applied Geophysics. 2024. DOI : 10.1016/j.jappgeo.2024.105453.Perfectly matched layers for the Boltzmann equation: Stability and sensitivity analysis
Journal Of Computational Physics. 2024. DOI : 10.1016/j.jcp.2024.113047.Machine-Learning-Enhanced Real-Time Aerodynamic Forces Prediction Based on Sparse Pressure Sensor Inputs
AIAA Journal. 2024. DOI : 10.2514/1.J063183.Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks
Journal Of Computational Physics. 2024. DOI : 10.1016/j.jcp.2024.112986.Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps
Computer Methods In Applied Mechanics And Engineering. 2024. DOI : 10.1016/j.cma.2024.116770.A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
Journal Of Computational Physics. 2024. DOI : 10.1016/j.jcp.2024.112762.Uncertainty quantification in groundwater volume predictions from seismic data using neural networks
2024. 30 European Meeting of Environmental and Engineering Geophysics, Helsinki, Finland, 2024-09-08 - 2024-09-12. DOI : 10.3997/2214-4609.202420086.A Fast Direct Solver for Higher Order Discretizations of Integral Equations
2024. IEEE International Symposium on Antennas and Propagation and INC/USNCURSI Radio Science Meeting, Florence, Italy, 2024-07-14 - 2024-07-19. p. 497 - 498. DOI : 10.1109/AP-S/INC-USNC-URSI52054.2024.10686430.2023
Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics
International Journal Of High Performance Computing Applications. 2023. DOI : 10.1177/10943420231208948.Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
Journal Of Computational Physics. 2023. DOI : 10.1016/j.jcp.2023.112621.Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation
Mathematics Of Computation. 2023. DOI : 10.1090/mcom/3885.Localized model order reduction and domain decomposition methods for coupled heterogeneous systems
International Journal For Numerical Methods In Engineering. 2023. DOI : 10.1002/nme.7295.A new variable shape parameter strategy for RBF approximation using neural networks
Computers & Mathematics With Applications. 2023. DOI : 10.1016/j.camwa.2023.05.005.An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
Computers & Fluids. 2023. DOI : 10.1016/j.compfluid.2023.105813.Reduced order models for coupled systems
Lausanne, EPFL, 2023. DOI : 10.5075/epfl-thesis-10208.Monitoring of water table level and volume of water in a porous storage by seismic data
2023. 29 European Meeting of Environmental and Engineering Geophysics, Edinburgh, United Kingdom, 2023-09-03 - 2023-09-07. DOI : 10.3997/2214-4609.202320058.2022
Multi-fidelity surrogate modeling using long short-term memory networks
Computer Methods In Applied Mechanics And Engineering. 2022. DOI : 10.1016/j.cma.2022.115811.Model order reduction for compressible flows solved using the discontinuous Galerkin methods
Journal Of Computational Physics. 2022. DOI : 10.1016/j.jcp.2022.111452.A data-driven shock capturing approach for discontinuous Galekin methods
Computers & Fluids. 2022. DOI : 10.1016/j.compfluid.2022.105592.Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows
Communications In Computational Physics. 2022. DOI : 10.4208/cicp.OA-2021-0180.Reduced basis methods for numerical room acoustic simulations with parametrized boundaries
Journal Of The Acoustical Society Of America. 2022. DOI : 10.1121/10.0012696.Discovery of Slow Variables in a Class Of Multiscale Stochastic Systems Via Neural Networks
Journal of Nonlinear Science. 2022. DOI : 10.1007/s00332-022-09808-7.Preface to the Focused Issue on WENO Schemes
Communications On Applied Mathematics And Computation. 2022. DOI : 10.1007/s42967-022-00196-z.Reduced basis methods for time-dependent problems
Acta Numerica. 2022. DOI : 10.1017/S0962492922000058.Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
Esaim-Mathematical Modelling And Numerical Analysis. 2022. DOI : 10.1051/m2an/2022013.Multi-fidelity regression using artificial neural networks: Efficient approximation of parameter-dependent output quantities
Computer Methods In Applied Mechanics And Engineering. 2022. DOI : 10.1016/j.cma.2021.114378.A hierarchical preconditioner for wave problems in quasilinear complexity
SIAM Journal on Scientific Computing. 2022. DOI : 10.1137/20M1365958.Preface to Focused Issue on Discontinuous Galerkin Methods PREFACE
Communications On Applied Mathematics And Computation. 2022. DOI : 10.1007/s42967-021-00170-1.Population pharmacokinetic model selection assisted by machine learning
Journal Of Pharmacokinetics And Pharmacodynamics. 2022. DOI : 10.1007/s10928-021-09793-6.Structure-preserving approaches and data-driven closure modeling for model order reduction
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9527.2021
Physics-informed machine learning for reduced-order modeling of nonlinear problems
Journal of Computational Physics. 2021. DOI : 10.1016/j.jcp.2021.110666.Construction of optimal spectral methods in phase retrieval
2021. 2nd Conference on Mathematical and Scientific Machine Learning (MSML 2021), Lausanne, Suisse, August 16-19, 2021. p. 693 - 720.Structure-Preserving Reduced Basis Methods For Poisson Systems
Mathematics Of Computation. 2021. DOI : 10.1090/mcom/3618.Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability
Communications In Computational Physics. 2021. DOI : 10.4208/cicp.OA-2020-0064.Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation
Advances In Computational Mathematics. 2021. DOI : 10.1007/s10444-021-09862-x.Fast screening of covariates in population models empowered by machine learning
Journal Of Pharmacokinetics And Pharmacodynamics. 2021. DOI : 10.1007/s10928-021-09757-w.Modeling synchronization in globally coupled oscillatory systems using model order reduction
Chaos: An Interdisciplinary Journal of Nonlinear Science. 2021. DOI : 10.1063/5.0031142.Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks
Journal Of Computational Physics. 2021. DOI : 10.1016/j.jcp.2021.110144.A phenomenological extended-reaction boundary model for time-domain wave-based acoustic simulations under sparse reflection conditions using a wave splitting method
Applied Acoustics. 2021. DOI : 10.1016/j.apacoust.2020.107596.Efficient algorithms for wave problems
Lausanne, EPFL, 2021. DOI : 10.5075/epfl-thesis-8641.Hybrid high-resolution RBF-ENO method
Journal of Computational Physics: X. 2021. DOI : 10.1016/j.jcpx.2021.100089.2020
A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations
Communications On Applied Mathematics And Computation. 2020. DOI : 10.1007/s42967-020-00065-7.Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)
Science China-Mathematics. 2020. 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. DOI : 10.1121/10.0002448.Controlling oscillations in spectral schemes using Artificial Neural Networks
2020Massive parallel nodal discontinuous Galerkin finite element method simulator for room acoustics
2020Apparent diffusion coefficient measured by diffusion MRI of moving and deforming domains
Journal of Magnetic Resonance. 2020. 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. DOI : 10.1016/j.cma.2020.113315.Conservative Model Order Reduction for Fluid Flow
Quantification of Uncertainty: Improving Efficiency and Technology; Cham: Springer, 2020.Physics-informed machine learning for reduced-order modeling of nonlinear problems
2020Rare event simulation for large-scale structures with local nonlinearities
Computer Methods In Applied Mechanics And Engineering. 2020. 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. DOI : 10.1007/s10915-020-01237-6.A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems
Computer Methods In Applied Mechanics And Engineering. 2020. DOI : 10.1016/j.cma.2020.112947.Constraint-aware neural networks for Riemann problems
Journal Of Computational Physics. 2020. 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. DOI : 10.1016/j.jcp.2020.109304.A Study of Several Artificial Viscosity Models within the Discontinuous Galerkin Framework
Communications In Computational Physics. 2020. DOI : 10.4208/cicp.OA-2019-0118.Simulation-based Anomaly Detection and Damage Localization: An application to Structural Health Monitoring
Computer Methods In Applied Mechanics And Engineering. 2020. DOI : 10.1016/j.cma.2020.112896.Two-Dimensional RBF-ENO Method on Unstructured Grids
Journal Of Scientific Computing. 2020. 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. DOI : 10.1007/s10915-020-01123-1.Effective diffusion tensor measured by diffusion MRI of moving and deforming domains
2020High-order essentially nonoscillatory methods based on radial basis functions
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-8411.RBF Based CWENO Method
2020. ICOSAHOM 2018, London, UK, July 9-13, 2018. p. 191 - 201. DOI : 10.1007/978-3-030-39647-3_14.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.Numerical methods for structural anomaly detection using model order reduction and data-driven techniques
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7734.Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method
The Journal of the Acoustical Society of America. 2020. DOI : 10.1121/10.0001170.2019
Modeling extended-reaction boundary conditions in time-domain wave-based simulations of room acoustics
2019Model order reduction for large-scale structures with local nonlinearities
Computer Methods in Applied Mechanics and Engineering. 2019. DOI : 10.1016/j.cma.2019.04.042.A comparative study of earthquake source models in high- order accurate tsunami simulations
Ocean Modelling. 2019. DOI : 10.1016/j.ocemod.2019.101429.Time domain room acoustic simulations using the spectral element method
Journal Of The Acoustical Society Of America. 2019. DOI : 10.1121/1.5109396.MATHICSE Technical Report: Time domain room acoustic simulations using a spectral element method
2019MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems
2019MATHICSE Technical Report: Simulation-Based Anomaly Detection and Damage Localization: an Application to Structural Health Monitoring
2019MATHICSE Technical Report: A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems
2019MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks
2019Structure-Preserving Model-Reduction of Dissipative Hamiltonian Systems
Journal of Scientific Computing. 2019. DOI : 10.1007/s10915-018-0653-6.A nodal discontinuous Galerkin finite element method for the poroelastic wave equation
Computational Geoscience. 2019. DOI : 10.1007/s10596-019-9809-1.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.Estimation of groundwater storage from seismic data using deep learning
Geophysical Research Letters. 2019. DOI : 10.1111/1365-2478.12831.Projective multiscale time-integration for electrostatic particle-in-cell methods
Computer Physics Communications. 2019. DOI : 10.1016/j.cpc.2018.10.012.Entropy stable essentially non-oscillatory methods based on RBF reconstructions
Mathematical Modeling and Numerical Analysis. 2019. DOI : 10.1051/m2an/2019011.2018
Detecting troubled-cells on two-dimensional unstructured grids using a neural network
Journal of Computational Physics. 2018. 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. DOI : 10.1016/j.cma.2018.10.029.Greedy Non-Intrusive Reduced Order Model for Fluid Dynamics
AIAA Journal. 2018. DOI : 10.2514/1.J056161.Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
Journal of Computational Physics. 2018. DOI : 10.1016/j.jcp.2019.01.031.POD-Kriging reduced method’s application in Tandem Cylinders’ flow
Journal of Northwestern Polytechnical University. 2018. DOI : 10.1051/jnwpu/20183620220.Research and Education in Computational Science and Engineering
Siam Review. 2018. DOI : 10.1137/16M1096840.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.Controlling oscillations in high-order schemes using neural networks
2018Discontinuous 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.Non-intrusive reduced order modeling of nonlinear problems using neural networks
Journal of Computational Physics. 2018. DOI : 10.1016/j.jcp.2018.02.037.Scaling and Resilience in Numerical Algorithms for Exascale Computing
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8926.Symplectic Model-Reduction with a Weighted Inner Product
2018Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure
Mathematics of computation. 2018.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.Geometric Model Order Reduction
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8923.An artificial neural network as a troubled-cell indicator
Journal of computational physics. 2018. DOI : 10.1016/j.jcp.2018.04.029.Flowfield Reconstruction Method Using Artificial Neural Network
AIAA Journal. 2018. DOI : 10.2514/1.J057108.2017
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.Large-Scale Tsunami Simulations using the Discontinuous Galerkin Method
27th Biennial Conference on Numerical Analysis, Glasgow, UK, June 27-30, 2017.High-Order Accurate Local Schemes for Fractional Differential Equations
Journal Of Scientific Computing. 2017. DOI : 10.1007/s10915-015-0089-1.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.A greedy non-intrusive reduced order model for fluid dynamics
Journal of Northwestern Polytechnical University. 2017.Adaptive WENO methods based on radial basis functions reconstruction
Journal of Scientific Computing. 2017. DOI : 10.1007/s10915-017-0383-1.A kernel compression scheme for fractional differential equations
Siam Journal on Numerical Analysis. 2017. DOI : 10.1137/15M1043960.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.Efficient Preconditioning of hp-FEM Matrices by Hierarchical Low-Rank Approximations
Journal Of Scientific Computing. 2017. DOI : 10.1007/s10915-016-0347-x.Numerical methods for conservation laws: From analysis to algorithms
Philadelphia: SIAM Publishing, 2017.Identification of a Predator-Prey System from Simulation Data of a Convection Model
Physics of Plasmas. 2017. DOI : 10.1063/1.4977057.A comparative study of shock capturing models for the discontinuous Galerkin method
2017Structure 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.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.Efficient Absorbing Layers for Weakly Compressible Flows
2016Spectral methods for tempered fractional differential equations
2016Spectral Methods for Hyperbolic Problems
Handbook of Numerical Methods for Hyperbolic Problems Basic and Fundamental Issues; Elsevier Publishing, 2016. p. 441 - 466.Fault Tolerance in the Parareal Method
2016. ACM Workshop on Fault-Tolerance for HPC at Extreme Scale (FTXS). p. 1 - 8. DOI : 10.1145/2909428.2909431.2015
Local discontinuous Galerkin methods for fractional ordinary differential equations
Bit Numerical Mathematics. 2015. DOI : 10.1007/s10543-014-0531-z.Reduced basis multiscale finite element methods for elliptic problems
Multiscale Modeling and Simulation. 2015. DOI : 10.1137/140955070.Modeling 3D Magma Dynamics Using a Discontinuous Galerkin Method
Communications in Computational Physics. 2015. DOI : 10.4208/cicp.090314.151214a.Certified Reduced Basis Methods for Parametrized Partial Differential Equations
Springer Verlag, 2015.Accuracy of high order and spectral methods for hyperbolic conservation laws with discontinuous solutions
Siam Journal on Numerical Analysis. 2015. DOI : 10.1137/140992758.Special Issue on "Fractional PDEs: Theory, Numerics, and Applications"
Journal Of Computational Physics. 2015. DOI : 10.1016/j.jcp.2015.04.007.A Parareal Method for Time-fractional Differential Equations
Journal of Computational Physics. 2015. DOI : 10.1016/j.jcp.2014.11.034.An Adjoint Approach for Stabilizing the Parareal Method
2015Nodal 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.A Multi-domain Spectral Method for Time-fractional Differential Equations
Journal of Computational Physics. 2015. DOI : 10.1016/j.jcp.2014.10.016.Hyperbolic Problems: Theory and Computation
Journal Of Scientific Computing. 2015. DOI : 10.1007/s10915-015-0065-9.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.Multilevel and Local Timestepping Discontinuous Galerkin Methods for Magma Dynamics
Computational Geosciences. 2015. DOI : 10.1007/s10596-015-9514-7.2014
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.Fast prediction and evaluation of gravitational waveforms using surrogate models
Physical Review X (PRX). 2014. DOI : 10.1103/PhysRevX.4.031006.Stable multi-domain spectral penalty methods for fractional partial differential equations
Journal of Computational Physics. 2014. DOI : 10.1016/j.jcp.2013.09.041.Discontinuous Galerkin method for fractional convection-diffusion equations
Siam Journal on Numerical Analysis. 2014. DOI : 10.1137/130918174.Model Reduction Opportunities in Detailed Simulations of Combustion Dynamics
2014. 52nd Aerospace Sciences Meeting. DOI : 10.2514/6.2014-0820.On the Use of Reduced Basis Methods to Accelerate and Stabilize the Parareal Method
2014. Workshop on Reduced Basis, POD and Reduced Order Methods for Model and Computational Reduction: towards Real-time Computing and Visualization', Lausanne, CH. p. 187 - 214. DOI : 10.1007/978-3-319-02090-7_7.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.Multiscale modeling of sound propagation through the lung parenchyma
Mathematical Modelling and Numerical Analysis. 2014. DOI : 10.1051/m2an/2013093.Time-domain finite element methods for Maxwell's equations in metamaterials
Siam Review. 2014.Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012
2014High-order multiscale finite element method for elliptic problems
Multiscale Modeling and Simulation. 2014. DOI : 10.1137/120898024.Applications of Model Reduction Techniques in Aerospace Combustors
2014. AIAA Conference.2013
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.Spectral methods: algorithms, analysis and applications [book review of MR2867779]
SIAM Review. 2013.High-order accurate methods for solving Maxwell's equations: Applications to photonic crystals and thin layer coatings
Saarbrucken, Germany: Scholar-Press, 2013.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/2013091.2012
High-Order Discontinuous Galerkin Methods by GPU Metaprogramming
GPU Solutions to Multi-scale Problems in Science and Engineering; Springer Verlag, 2012. p. 353 - 374.Certified Reduced Basis Method for the Electric Field Integral Equation
SIAM Journal on Scientific Computing. 2012. DOI : 10.1137/110848268.Numerical simulations with a first-order BSSN formulation of Einstein's field equations
Physical Review D [1970-2015]. 2012. DOI : 10.1103/PhysRevD.85.084004.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.Computation of connection coefficients and measure modifications for orthogonal polynomials
BIT Numerical Mathematics. 2012. DOI : 10.1007/s10543-011-0363-z.Sparse Gradient Image Reconstruction from Incomplete Fourier Measurements and Prior Edge Information
2012A reduced basis method for electromagnetic scattering by multiple particles in three dimensions
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Mathematical Modeling and Numerical Analysis. 2012. DOI : 10.1051/m2an/2011066.Solving Wave Equations on Unstructured Geometries
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Spectral and High Order Methods for Partial Differential Equations : Selected papers from the ICOSAHOM '09 conference, June 22-26, Trondheim, Norway
2011Modeling Magma Dynamics with a Mixed Fourier Collocation - Discontinuous Galerkin Method
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Mathematics of Computation. 2011. DOI : 10.1090/S0025-5718-2010-02437-8.Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty
Communications in Computational Physics. 2011. DOI : 10.4208/cicp.090110.080910a.Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty
Applied Numerical Mathematics. 2011. DOI : 10.1016/j.apnum.2010.08.002.The reduced basis method for the electric field integral equation
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Geophysical Research Letters. 2010. DOI : 10.1029/2010GL044162.Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations
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ESAIM: Mathematical Modelling and Numerical Analysis. 2009. DOI : 10.1051/m2an/2009037.Discontinuous Galerkin method for computing gravitational waveforms from extreme mass ratio binaries
Classical and Quantum Gravity. 2009. DOI : 10.1088/0264-9381/26/16/165010.High-order accurate thin layer approximations for time-domain electromagnetics. Part I: General metal backed coatings
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IEEE Transactions on Electromagnetic Compatibility. 2009. DOI : 10.1109/TEMC.2009.2015056.IMEX Evolution of Scalar Fields on Curved Backgrounds
Communications in Computational Physics. 2009. DOI : 10.4208/cicp.2009.v6.p1063.2008
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Coastal Engineering. 2008. DOI : 10.1016/j.coastaleng.2007.09.005.Nodal discontinuous Galerkin methods: Algorithms, analysis and applications
Springer, 2008.PDE constrained optimization and design of frozen mode crystals
Communications in Computational Physics. 2008.Biased liquid crystal photonic bandgap fiber
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Mathematics of Computation. 2008. DOI : 10.1090/S0025-5718-08-02110-8.A monotonic evaluation of lower bounds for inf-sup stability constants in the frame of reduced basis approximations
Comptes Rendus Mathematique. 2008. DOI : 10.1016/j.crma.2008.10.012.Numerical modeling of double-layered piezoelectric transducer systems using a high-order discontinuous Galerkin method
Computers & Structures. 2008. DOI : 10.1016/j.compstruc.2008.02.006.A Fast and Parallel Stroud-Based Stochastic Collocation Method for Statistical EMI/EMC Analysis
2008. IEEE International Symposium on Electromagnetic Compatibility, Detroit, MI, AUG 18-22, 2008. p. 790 - 794. DOI : 10.1109/ISEMC.2008.4652151.2007
Spectral methods for time-dependent problems
Cambridge University Press, 2007.Predicting transport by Lagrangian coherent structures with a high-order method
Theoretical and Computational Fluid Dynamics. 2007. DOI : 10.1007/s00162-006-0031-0.Developments in overlapping Schwarz preconditioning of high-order nodal discontinuous Galerkin discretizations
Domain decomposition methods in science and engineering XVI; Springer, 2007. p. 325 - 332.Proceedings of the 7th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'05)
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Communications in Computational Physics. 2007.Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
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Pade-legendre interpolants for Gibbs reconstruction
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Springer Publishing, 2006.Computational modeling of uncertainty in time-domain electromagnetics
SIAM Journal on Scientific Computing. 2006. DOI : 10.1137/040621673.High-order nodal discontinuous Galerkin particle-in-cell method on unstructured grids
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Computer Methods in Applied Mechanics and Engineering. 2006. DOI : 10.1016/j.cma.2006.06.020.Reduced Navier-Stokes equations near a flow boundary
Physica D. 2006. DOI : 10.1016/j.physd.2006.04.008.Idempotent filtering in spectral and spectral element methods
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2006. 6th International Conference on Spectral and High-Order Methods.Simulations of the weibel instability with a high-order discontinuous galerkin particle-in-cell solver
2006. 44th AIAA Aerospace Sciences Meeting, Reno, NV. p. 14189 - 14199. DOI : 10.2514/6.2006-1171.Nodal DG-FEM solution of high-order Boussinesq-type equations
Journal of Engineering Mathematics. 2006. DOI : 10.1007/s10665-006-9064-z.2005
Analytical and numerical study on grating depth effects in grating coupled waveguide sensors
Applied Physics B. 2005. DOI : 10.1007/s00340-005-1841-2.High-order collocation methods for differential equations with random inputs
SIAM Journal on Scientific Computing. 2005. DOI : 10.1137/040615201.Computational modeling of uncertainty in time-domain electromagnetics
2005. 2005 Workshop on Computational Electromagnetics in Time-Domain, CEM-TD 2005, Atlanta, GA, SEP 12-14, 2005. p. 32 - 35. DOI : 10.1109/CEMTD.2005.1531705.Uncertainty analysis for the steady-state flows in a dual throat nozzle
Journal of Computational Physics. 2005. DOI : 10.1016/j.jcp.2004.10.019.Proceedings of AFOSR Workshop on Advances and Challenges in Time-Integration of PDE's
2005. AFOSR Workshop on Advances and Challenges in Time-Integration of PDE's.A spectral multidomain penalty method model for the simulation of high Reynolds number localized incompressible stratified turbulence
Journal of Computational Physics. 2005. DOI : 10.1016/j.jcp.2004.07.007.Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs
SIAM Journal on Numerical Analysis. 2005. DOI : 10.1137/S0036142903432425.2004
Discontinuous Galerkin methods for the time-domain Maxwell's equations
ACES Newsletter. 2004.Fast and accurate boundary variation method for multilayered diffraction optics
Journal of the Optical Society of America A: Optics, Image Science and Vision. 2004. DOI : 10.1364/JOSAA.21.000757.Pade-Jacobi Approximants
2004High-order accurate methods for time-domain electromagnetics
Computer Modeling in Engineering & Sciences. 2004. DOI : 10.3970/cmes.2004.005.395.High-order nodal discontinuous Galerkin methods for the Maxwell eigenvalue problem
Philosophical Transactions of the Royal Society of London A. 2004. DOI : 10.1098/rsta.2003.1332.2003
High-order accurate methods in time-domain computational electromagnetics: A review
Advances in Imaging and Electron Physics, Vol 127; Elsevier, 2003. p. 59 - 123.On the constants in hp-finite element trace inverse inequalities
Computer Methods in Applied Mechanics and Engineering. 2003. DOI : 10.1016/S0045-7825(03)00294-9.High-order localized time integration for grid-induced stiffness
2003. 2nd MIT Conference on Computational Fluid and Solid Mechanics, MIT, CAMBRIDGE, MA, JUN 17-20, 2003. p. 1883 - 1886. DOI : 10.1016/B978-008044046-0.50461-9.2002
A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries
Ultrasonics. 2002. DOI : 10.1016/S0041-624X(02)00133-6.Multidomain pseudospectral time-domain simulations of scattering by objects buried in lossy media
IEEE Transactions on Geoscience and Remote Sensing. 2002. DOI : 10.1109/TGRS.2002.800272.Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
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Journal of Computational Physics. 2002. DOI : 10.1006/jcph.2002.7118.Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics
Journal of Scientific Computing. 2002. DOI : 10.1023/A:1015141823608.2001
Staircase-free finite-difference time-domain formulation for general materials in complex geometries
IEEE Transactions on Antennas and Propagation. 2001. DOI : 10.1109/8.929629.Multi-domain pseudospectral time-domain method for lossy media
2001. IEEE Antennas and Propagation Society, AP-S International Symposium (Digest), Boston, MA. p. 842 - 845. DOI : 10.1109/APS.2001.959597.Spectral methods for hyperbolic problems
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Journal of Computational Physics. 2001. DOI : 10.1006/jcph.2001.6719.Fast and accurate modeling of waveguide grating couplers. II. Three-dimensional vectorial case
Journal of the Optical Society of America A: Optics, Image Science and Vision. 2001. DOI : 10.1364/JOSAA.18.002876.2000
Fast and accurate modeling of waveguide grating couplers
Journal of the Optical Society of America A: Optics, Image Science and Vision. 2000. DOI : 10.1364/JOSAA.17.001565.Rigorous three-dimensional analysis of surface-relief gratings using a spectral collocation method
2000. SPIE 3951, Diffractive/Holographic Technologies and Spatial Light Modulators VII, Bellingham, WA. p. 2 - 10. DOI : 10.1117/12.379350.Proceedings of the 4th International Conference on Spectral and High-Order Methods (ICOSAHOM'98)
2000. 4th International Conference on Spectral and High-Order Methods.Multidomain pseudospectral computation of Maxwell's equations in 3-D general curvilinear coordinates
Applied Numerical Mathematics. 2000. DOI : 10.1016/S0168-9274(99)00094-X.Stable spectral methods on tetrahedral elements
SIAM Journal on Scientific Computing. 2000. DOI : 10.1137/S1064827598343723.Rigorous analysis of focusing grating couplers using a time-domain spectral collocation method
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Applied Numerical Mathematics. 2000. DOI : 10.1016/S0168-9274(99)00084-7.Spectral penalty methods
Applied Numerical Mathematics. 2000. DOI : 10.1016/S0168-9274(99)00068-9.Ground states of dispersion-managed nonlinear Schrodinger equation
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Stable spectral methods for conservation laws on triangles with unstructured grids
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IEEE Transactions on Antennas and Propagation. 1999. DOI : 10.1109/8.753003.1998
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2024
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Journal Of Computational Physics. 2024-07-15. DOI : 10.1016/j.jcp.2024.113047.* Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks
Journal Of Computational Physics. 2024-07-01. DOI : 10.1016/j.jcp.2024.112986.* Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps
Computer Methods In Applied Mechanics And Engineering. 2024-01-18. DOI : 10.1016/j.cma.2024.116770.* A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
Journal Of Computational Physics. 2024-01-17. DOI : 10.1016/j.jcp.2024.112762.2023
* Massively parallel nodal discontinous Galerkin finite element method simulator for room acoustics
International Journal Of High Performance Computing Applications. 2023-11-16. DOI : 10.1177/10943420231208948.* Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
Journal Of Computational Physics. 2023-11-15. DOI : 10.1016/j.jcp.2023.112621.* Adaptive Symplectic Model Order Reduction Of Parametric Particle-Based Vlasov-Poisson Equation
Mathematics Of Computation. 2023-08-24. DOI : 10.1090/mcom/3885.* Localized model order reduction and domain decomposition methods for coupled heterogeneous systems
International Journal For Numerical Methods In Engineering. 2023-05-25. DOI : 10.1002/nme.7295.* A new variable shape parameter strategy for RBF approximation using neural networks
Computers & Mathematics With Applications. 2023-05-23. DOI : 10.1016/j.camwa.2023.05.005.* An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
Computers & Fluids. 2023-02-08. DOI : 10.1016/j.compfluid.2023.105813.2022
* Model order reduction for compressible flows solved using the discontinuous Galerkin methods
Journal Of Computational Physics. 2022-11-01. DOI : 10.1016/j.jcp.2022.111452.* A data-driven shock capturing approach for discontinuous Galekin methods
Computers & Fluids. 2022-09-15. DOI : 10.1016/j.compfluid.2022.105592.* Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows
Communications In Computational Physics. 2022-09-01. DOI : 10.4208/cicp.OA-2021-0180.* Reduced basis methods for numerical room acoustic simulations with parametrized boundaries
Journal Of The Acoustical Society Of America. 2022-08-01. DOI : 10.1121/10.0012696.* Discovery of Slow Variables in a Class Of Multiscale Stochastic Systems Via Neural Networks
Journal of Nonlinear Science. 2022-08-01. DOI : 10.1007/s00332-022-09808-7.* Preface to the Focused Issue on WENO Schemes
Communications On Applied Mathematics And Computation. 2022-05-13. DOI : 10.1007/s42967-022-00196-z.* Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
Esaim-Mathematical Modelling And Numerical Analysis. 2022-03-08. DOI : 10.1051/m2an/2022013.* Multi-fidelity regression using artificial neural networks: Efficient approximation of parameter-dependent output quantities
Computer Methods In Applied Mechanics And Engineering. 2022-02-01. DOI : 10.1016/j.cma.2021.114378.* A hierarchical preconditioner for wave problems in quasilinear complexity
SIAM Journal on Scientific Computing. 2022-01-27. DOI : 10.1137/20M1365958.* Population pharmacokinetic model selection assisted by machine learning
Journal Of Pharmacokinetics And Pharmacodynamics. 2022. DOI : 10.1007/s10928-021-09793-6.* Preface to Focused Issue on Discontinuous Galerkin Methods PREFACE
Communications On Applied Mathematics And Computation. 2022. DOI : 10.1007/s42967-021-00170-1.2021
* Physics-informed machine learning for reduced-order modeling of nonlinear problems
Journal of Computational Physics. 2021-08-27. DOI : 10.1016/j.jcp.2021.110666.* Structure-Preserving Reduced Basis Methods For Poisson Systems
Mathematics Of Computation. 2021-07-01. DOI : 10.1090/mcom/3618.* Non-Intrusive Reduced Order Modeling of Convection Dominated Flows Using Artificial Neural Networks with Application to Rayleigh-Taylor Instability
Communications In Computational Physics. 2021-07-01. DOI : 10.4208/cicp.OA-2020-0064.* Pointwise error estimate in difference setting for the two-dimensional nonlinear fractional complex Ginzburg-Landau equation
Advances In Computational Mathematics. 2021-06-01. DOI : 10.1007/s10444-021-09862-x.* Fast screening of covariates in population models empowered by machine learning
Journal Of Pharmacokinetics And Pharmacodynamics. 2021-05-21. DOI : 10.1007/s10928-021-09757-w.* Modeling synchronization in globally coupled oscillatory systems using model order reduction
Chaos. 2021-05-01. DOI : 10.1063/5.0031142.* Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks
Journal Of Computational Physics. 2021-04-15. DOI : 10.1016/j.jcp.2021.110144.* A phenomenological extended-reaction boundary model for time-domain wave-based acoustic simulations under sparse reflection conditions using a wave splitting method
Applied Acoustics. 2021-01-15. DOI : 10.1016/j.apacoust.2020.107596.* Hybrid high-resolution RBF-ENO method
Journal of Computational Physics: X. 2021. DOI : 10.1016/j.jcpx.2021.100089.2020
* A Local Discontinuous Galerkin Method for Two-Dimensional Time Fractional Diffusion Equations
Communications On Applied Mathematics And Computation. 2020-12-01. DOI : 10.1007/s42967-020-00065-7.* 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.* Massive parallel nodal discontinuous Galerkin finite element method simulator for room acoustics
International Journal of High Performance Computing Applications. 2020-09-06.* 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.* Conservative Model Order Reduction for Fluid Flow
Quantification of Uncertainty: Improving Efficiency and Technology; Cham: Springer, 2020-07-31. p. 282.* Physics-informed machine learning for reduced-order modeling of nonlinear problems
2020-07-23.* 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.* A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems
Computer Methods In Applied Mechanics And Engineering. 2020-06-01. DOI : 10.1016/j.cma.2020.112947.* 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.* 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.* Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method
The Journal of the Acoustical Society of America. 2020. DOI : 10.1121/10.0001170.* 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
* 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.* 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.* Entropy stable essentially non-oscillatory methods based on RBF reconstructions
Mathematical Modeling and Numerical Analysis. 2019. DOI : 10.1051/m2an/2019011.* A nodal discontinuous Galerkin finite element method for the poroelastic wave equation
Computational Geoscience. 2019. DOI : 10.1007/s10596-019-9809-1.* 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. 2018-10-01. DOI : 10.1016/j.cma.2018.10.029.* Greedy Non-Intrusive Reduced Order Model for Fluid Dynamics
AIAA Journal. 2018-06-24. DOI : 10.2514/1.J056161.* 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. DOI : 10.1051/jnwpu/20183620220.* Structure-Preserving Reduced Basis Methods for Hamiltonian Systems with a State-dependent Poisson Structure
Mathematics of computation. 2018.* 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.Teaching & PhD
PhD Students
Past EPFL PhD Students
Babak Maboudi Afkham, Allan Svejstrup Nielsen, Caterina Bigoni, Fabian Mönkeberg, Boris Bonev, Nicolò Ripamonti, Niccolo' Discacciati