A Theoretical Analysis of Deep Neural Networks and Parametric PDEs

31 March 2019

Papers citing "A Theoretical Analysis of Deep Neural Networks and Parametric PDEs"

38 / 38 papers shown

Title
Reduced Order Models and Conditional Expectation -- Analysing Parametric Low-Order Approximations Hermann G. Matthies 42 0 0 17 Feb 2025
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation Janina Enrica Schutte Martin Eigel AI4CE 29 2 0 19 Mar 2024
Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Models Anant Raj Umut Simsekli Alessandro Rudi DiffM 31 1 0 30 Mar 2023
Limitations of neural network training due to numerical instability of backpropagation Clemens Karner V. Kazeev P. Petersen 40 3 0 03 Oct 2022
Approximation results for Gradient Descent trained Shallow Neural Networks in $1d$ R. Gentile G. Welper ODL 56 6 0 17 Sep 2022
Error analysis for deep neural network approximations of parametric hyperbolic conservation laws Tim De Ryck Siddhartha Mishra PINN 15 10 0 15 Jul 2022
Deep surrogate accelerated delayed-acceptance HMC for Bayesian inference of spatio-temporal heat fluxes in rotating disc systems Teo Deveney E. Mueller T. Shardlow AI4CE 27 0 0 05 Apr 2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations Tim De Ryck Ameya Dilip Jagtap S. Mishra PINN 49 115 0 17 Mar 2022
The Mathematics of Artificial Intelligence Gitta Kutyniok 22 0 0 16 Mar 2022
A machine learning approach for fighting the curse of dimensionality in global optimization J. Schumann Alejandro M. Aragón 28 2 0 28 Oct 2021
An artificial neural network approach to bifurcating phenomena in computational fluid dynamics F. Pichi F. Ballarin G. Rozza J. Hesthaven AI4CE 38 71 0 22 Sep 2021
Learning Density Distribution of Reachable States for Autonomous Systems Yue Meng Dawei Sun Zeng Qiu Md Tawhid Bin Waez Chuchu Fan 77 19 0 14 Sep 2021
Variational Physics Informed Neural Networks: the role of quadratures and test functions S. Berrone C. Canuto Moreno Pintore 31 41 0 05 Sep 2021
Designing Rotationally Invariant Neural Networks from PDEs and Variational Methods Tobias Alt Karl Schrader Joachim Weickert Pascal Peter M. Augustin 22 4 0 31 Aug 2021
Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques T. Kadeethum F. Ballarin Y. Cho Daniel O’Malley H. Yoon N. Bouklas AI4CE 18 61 0 23 Jul 2021
Cell-average based neural network method for hyperbolic and parabolic partial differential equations Changxin Qiu Jue Yan 16 10 0 02 Jul 2021
Error analysis for physics informed neural networks (PINNs) approximating Kolmogorov PDEs Tim De Ryck Siddhartha Mishra PINN 21 100 0 28 Jun 2021
Random feature neural networks learn Black-Scholes type PDEs without curse of dimensionality Lukas Gonon 21 35 0 14 Jun 2021
Two-layer neural networks with values in a Banach space Yury Korolev 29 23 0 05 May 2021
On the approximation of functions by tanh neural networks Tim De Ryck S. Lanthaler Siddhartha Mishra 26 138 0 18 Apr 2021
Proof of the Theory-to-Practice Gap in Deep Learning via Sampling Complexity bounds for Neural Network Approximation Spaces Philipp Grohs F. Voigtlaender 31 34 0 06 Apr 2021
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations N. R. Franco Andrea Manzoni P. Zunino 26 45 0 10 Mar 2021
Parametric Complexity Bounds for Approximating PDEs with Neural Networks Tanya Marwah Zachary Chase Lipton Andrej Risteski 28 19 0 03 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 21 212 0 28 Jan 2021
An overview on deep learning-based approximation methods for partial differential equations C. Beck Martin Hutzenthaler Arnulf Jentzen Benno Kuckuck 30 146 0 22 Dec 2020
Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data Ben Adcock Simone Brugiapaglia N. Dexter S. Moraga 36 29 0 11 Dec 2020
Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems Donsub Rim Luca Venturi Joan Bruna Benjamin Peherstorfer 28 9 0 28 Jul 2020
Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions Philipp Grohs L. Herrmann 30 52 0 10 Jul 2020
Expressivity of Deep Neural Networks Ingo Gühring Mones Raslan Gitta Kutyniok 16 51 0 09 Jul 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 29 19 0 03 Jun 2020
Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation Arnulf Jentzen Timo Welti 22 15 0 03 Mar 2020
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs S. Fresca Luca Dede' Andrea Manzoni AI4CE 28 258 0 12 Jan 2020
Uniform error estimates for artificial neural network approximations for heat equations Lukas Gonon Philipp Grohs Arnulf Jentzen David Kofler David Siska 29 34 0 20 Nov 2019
Space-time error estimates for deep neural network approximations for differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philipp Zimmermann 29 33 0 11 Aug 2019
Deep splitting method for parabolic PDEs C. Beck S. Becker Patrick Cheridito Arnulf Jentzen Ariel Neufeld 23 125 0 08 Jul 2019
Data driven approximation of parametrized PDEs by Reduced Basis and Neural Networks N. D. Santo S. Deparis Luca Pegolotti 19 66 0 02 Apr 2019
Unbiased deep solvers for linear parametric PDEs Marc Sabate Vidales David Siska Lukasz Szpruch OOD 32 7 0 11 Oct 2018
Solving the Kolmogorov PDE by means of deep learning C. Beck S. Becker Philipp Grohs Nor Jaafari Arnulf Jentzen 19 91 0 01 Jun 2018