Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

10 July 2020

Papers citing "Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions"

21 / 21 papers shown

Title
From Equations to Insights: Unraveling Symbolic Structures in PDEs with LLMs Rohan Bhatnagar Ling Liang Krish Patel Haizhao Yang 36 0 0 13 Mar 2025
Sampling Complexity of Deep Approximation Spaces Ahmed Abdeljawad Philipp Grohs 26 1 0 20 Dec 2023
Residual Multi-Fidelity Neural Network Computing Owen Davis Mohammad Motamed Raúl Tempone 37 1 0 05 Oct 2023
$A numerical approach for the fractional Laplacian via deep neural networks$ A numerical approach for the fractional Laplacian via deep neural networks Nicolás Valenzuela 29 3 0 30 Aug 2023
Theoretical guarantees for neural control variates in MCMC Denis Belomestny Artur Goldman A. Naumov S. Samsonov BDL DRL 13 6 0 03 Apr 2023
Multilevel CNNs for Parametric PDEs Cosmas Heiß Ingo Gühring Martin Eigel AI4CE 17 8 0 01 Apr 2023
Neural Network Approximations of PDEs Beyond Linearity: A Representational Perspective Tanya Marwah Zachary Chase Lipton Jianfeng Lu Andrej Risteski 49 10 0 21 Oct 2022
From Monte Carlo to neural networks approximations of boundary value problems L. Beznea Iulian Cîmpean Oana Lupascu-Stamate Ionel Popescu A. Zarnescu 14 1 0 03 Sep 2022
Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning Lorenz Richter Julius Berner 19 19 0 21 Jun 2022
Compressive Fourier collocation methods for high-dimensional diffusion equations with periodic boundary conditions Weiqi Wang Simone Brugiapaglia 19 2 0 02 Jun 2022
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent Yiping Lu Jose H. Blanchet Lexing Ying 35 7 0 15 May 2022
FinNet: Solving Time-Independent Differential Equations with Finite Difference Neural Network Son N. T. Tu Thu Nguyen AI4CE 13 0 0 18 Feb 2022
Exponential Convergence of Deep Operator Networks for Elliptic Partial Differential Equations C. Marcati Christoph Schwab 14 38 0 15 Dec 2021
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems Nikolas Nusken Lorenz Richter PINN DiffM 31 27 0 07 Dec 2021
Approximation properties of Residual Neural Networks for Kolmogorov PDEs Jonas Baggenstos Diyora Salimova 15 3 0 30 Oct 2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces Ziang Chen Jianfeng Lu Yulong Lu 32 26 0 14 Jun 2021
Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations Philipp Grohs L. Herrmann 9 6 0 09 Mar 2021
Parametric Complexity Bounds for Approximating PDEs with Neural Networks Tanya Marwah Zachary Chase Lipton Andrej Risteski 20 19 0 03 Mar 2021
Quantitative approximation results for complex-valued neural networks A. Caragea D. Lee J. Maly G. Pfander F. Voigtlaender 13 5 0 25 Feb 2021
Approximations with deep neural networks in Sobolev time-space Ahmed Abdeljawad Philipp Grohs 16 12 0 23 Dec 2020
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