335 citations · 1.8k across the 47 of their papers we have counts for
49 papers
Nonlinear model reduction for transport-dominated problems
Jan S. Hesthaven, Benjamin Peherstorfer, Benjamin Unger
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-d…
Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
Matteo Caldana, Jan S. Hesthaven
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog t…
GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications
Oisín M. Morrison, Federico Pichi, Jan S. Hesthaven
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…
Neural empirical interpolation method for nonlinear model reduction
Max Hirsch, Federico Pichi, Jan S. Hesthaven
In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the tim…
Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction
Nicola Rares Franco, Andrea Manzoni, Paolo Zunino +1
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial diffe…
Fast Numerical Approximation of Linear, Second-Order Hyperbolic Problems Using Model Order Reduction and the Laplace Transform
Fernando Henriquez, Jan S. Hesthaven
We extend our previous work [F. Henr'iquez and J. S. Hesthaven, arXiv:2403.02847 (2024)] to the linear, second-order wave equation in bounded domains. This technique uses two widel…
Fast Numerical Approximation of Parabolic Problems Using Model Order Reduction and the Laplace Transform
Fernando Henríquez, Jan S. Hesthaven
We introduce a method for the fast numerical approximation of linear, second-order parabolic partial differential equations (PDEs for short) with time-independent coefficients base…
Perfectly matched layers for the Boltzmann equation: stability and sensitivity analysis
Marco Sutti, Jan S. 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 l…
Positional Embeddings for Solving PDEs with Evolutional Deep Neural Networks
Mariella Kast, Jan S Hesthaven
This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric stru…
Machine learning enhanced real-time aerodynamic forces prediction based on sparse pressure sensor inputs
Junming Duan, Qian Wang, Jan S. Hesthaven
Accurate prediction of aerodynamic forces in real-time is crucial for autonomous navigation of unmanned aerial vehicles (UAVs). This paper presents a data-driven aerodynamic force…
A graph convolutional autoencoder approach to model order reduction for parametrized PDEs
Federico Pichi, Beatriz Moya, Jan S. Hesthaven
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…
Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems
Junming Duan, Jan S. Hesthaven
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 parametrize…
Monitoring of water volume in a porous reservoir using seismic data: A 3D simulation study
Mahnaz Khalili, Peter Göransson, Jan S. Hesthaven +3
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 i…
A new variable shape parameter strategy for RBF approximation using neural networks
Fatemeh Nassajian Mojarrad, Maria Han Veiga, Jan S. Hesthaven +1
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 ill-condition of the int…
Multi-fidelity surrogate modeling using long short-term memory networks
Paolo Conti, Mengwu Guo, Andrea Manzoni +1
When evaluating quantities of interest that depend on the solutions to differential equations, we inevitably face the trade-off between accuracy and efficiency. Especially for para…
Adaptive symplectic model order reduction of parametric particle-based Vlasov-Poisson equation
Jan S. Hesthaven, Cecilia Pagliantini, 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 exacerba…
FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment
Oscar P. Bruno, Jan S. Hesthaven, Daniel V. Leibovici
This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on…
Structure-preserving model order reduction of Hamiltonian systems
J. S. Hesthaven, C. Pagliantini, N. Ripamonti
We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many hig…
An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
Federico Pichi, Francesco Ballarin, Gianluigi Rozza +1
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 de…
A hierarchical preconditioner for wave problems in quasilinear complexity
Boris Bonev, Jan S. Hesthaven
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and disconti…
Discovery of slow variables in a class of multiscale stochastic systems via neural networks
Przemyslaw Zielinski, Jan S. Hesthaven
Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numeric…
Reduced basis methods for numerical room acoustic simulations with parametrized boundaries
Hermes Sampedro Llopis, Allan P. Engsig-Karup, Cheol-Ho Jeong +2
The use of model-based numerical simulation of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iterat…
Multi-fidelity regression using artificial neural networks: efficient approximation of parameter-dependent output quantities
Mengwu Guo, Andrea Manzoni, Maurice Amendt +2
Highly accurate numerical or physical experiments are often time-consuming or expensive to obtain. When time or budget restrictions prohibit the generation of additional data, the…
Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
Jan S. Hesthaven, Cecilia Pagliantini, Nicolò Ripamonti
This work proposes an adaptive structure-preserving model order reduction method for finite-dimensional parametrized Hamiltonian systems modeling non-dissipative phenomena. To over…