A practical existence theorem for reduced order models based on convolutional autoencoders

1 February 2024

Papers citing "A practical existence theorem for reduced order models based on convolutional autoencoders"

18 / 18 papers shown

Title
Learning smooth functions in high dimensions: from sparse polynomials to deep neural networks Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 49 4 0 04 Apr 2024
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields N. R. Franco Daniel Fraulin Andrea Manzoni P. Zunino AI4CE 37 4 0 18 Oct 2023
Operator learning with PCA-Net: upper and lower complexity bounds S. Lanthaler 41 25 0 28 Mar 2023
Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method F. Romor G. Stabile G. Rozza 40 23 0 01 Mar 2022
Neural Operator: Learning Maps Between Function Spaces Nikola B. Kovachki Zong-Yi Li Burigede Liu Kamyar Azizzadenesheli K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 103 448 0 19 Aug 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 59 45 0 10 Mar 2021
POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition S. Fresca Andrea Manzoni AI4CE 56 214 0 28 Jan 2021
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 70 29 0 11 Dec 2020
Fourier Neural Operator for Parametric Partial Differential Equations Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 484 2,397 0 18 Oct 2020
Deep learning of thermodynamics-aware reduced-order models from data Quercus Hernandez Alberto Badías D. González Francisco Chinesta Elías Cueto PINN AI4CE 36 79 0 03 Jul 2020
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences Siddhartha Mishra T. Konstantin Rusch 68 50 0 26 May 2020
The gap between theory and practice in function approximation with deep neural networks Ben Adcock N. Dexter 44 93 0 16 Jan 2020
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs S. Fresca Luca Dede' Andrea Manzoni AI4CE 56 262 0 12 Jan 2020
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 224 2,119 0 08 Oct 2019
Nonlinear Approximation and (Deep) ReLU Networks Ingrid Daubechies Ronald A. DeVore S. Foucart Boris Hanin G. Petrova 100 141 0 05 May 2019
A Theoretical Analysis of Deep Neural Networks and Parametric PDEs Gitta Kutyniok P. Petersen Mones Raslan R. Schneider 63 198 0 31 Mar 2019
Equivalence of approximation by convolutional neural networks and fully-connected networks P. Petersen Felix Voigtländer 54 79 0 04 Sep 2018
The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks Jonathan Frankle Michael Carbin 225 3,461 0 09 Mar 2018