Zobrazeno 1 - 10
of 559
pro vyhledávání: '"Hesthaven, Jan S"'
Autor:
Caldana, Matteo, Hesthaven, Jan S.
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying neural OD
Externí odkaz:
http://arxiv.org/abs/2408.06073
We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the construction of a
Externí odkaz:
http://arxiv.org/abs/2406.13567
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 this work, the graph feedforward network, which extends the concept o
Externí odkaz:
http://arxiv.org/abs/2406.03569
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 time complexity of computing the nonlinear term in a reduced order model
Externí odkaz:
http://arxiv.org/abs/2406.03562
Autor:
Henriquez, Fernando, Hesthaven, Jan S.
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, referred to as the Laplace Transform Reduced Basis (LT-RB) method, uses two widely
Externí odkaz:
http://arxiv.org/abs/2405.19896
Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction of a deep
Externí odkaz:
http://arxiv.org/abs/2404.18841
Autor:
Henríquez, Fernando, Hesthaven, Jan S.
We introduce a novel, fast method for the numerical approximation of parabolic partial differential equations (PDEs for short) based on model order reduction techniques and the Laplace transform. We start by applying said transform to the evolution p
Externí odkaz:
http://arxiv.org/abs/2403.02847
Autor:
Khalili, Mahnaz, Brodic, Bojan, Göransson, Peter, Heinonen, Suvi, Hesthaven, Jan S., Pasanen, Antti, Vauhkonen, Marko, Yadav, Rahul, Lähivaara, Timo
As global groundwater levels continue to decline rapidly, there is a growing need for advanced techniques to monitor and manage aquifers effectively. This study focuses on validating a numerical model using seismic data from a small-scale experimenta
Externí odkaz:
http://arxiv.org/abs/2312.14605
Autor:
Sutti, Marco, Hesthaven, Jan S.
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 layer (PML) technique. To ensure stability, we discard some parameters
Externí odkaz:
http://arxiv.org/abs/2312.03273
Autor:
Kast, Mariella, Hesthaven, Jan S
This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on eigenfunctions of
Externí odkaz:
http://arxiv.org/abs/2308.03461