335 citations · 1.8k across the 47 of their papers we have counts for
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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…