9 papers
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…
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…
Fast Numerical Approximation of Parabolic Problems Using Model Order Reduction and the Laplace Transform
Fernando HenrÃquez, 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…
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…
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…
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…