A unified deep artificial neural network approach to partial differential equations in complex geometries

17 November 2017

Papers citing "A unified deep artificial neural network approach to partial differential equations in complex geometries"

50 / 75 papers shown

Title
Reliable and Efficient Inverse Analysis using Physics-Informed Neural Networks with Distance Functions and Adaptive Weight Tuning Shota Deguchi Mitsuteru Asai PINN AI4CE 81 0 0 25 Apr 2025
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
Artificial Intelligence in Reactor Physics: Current Status and Future Prospects Ruizhi Zhang Shengfeng Zhu K. Wang Ding She J. Argaud B. Bouriquet Qing Li Helin Gong AI4CE 44 0 0 04 Mar 2025
Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases Madison Cooley Varun Shankar Robert M. Kirby Shandian Zhe 24 2 0 04 Oct 2024
Deterministic and statistical calibration of constitutive models from full-field data with parametric physics-informed neural networks D. Anton Jendrik-Alexander Tröger Henning Wessels Ulrich Römer Alexander Henkes Stefan Hartmann AI4CE 33 4 0 28 May 2024
Approximation of Solution Operators for High-dimensional PDEs Nathan Gaby Xiaojing Ye 19 0 0 18 Jan 2024
Neural Stream Functions Skylar W. Wurster Hanqi Guo Tom Peterka Han-Wei Shen 17 0 0 16 Jul 2023
A Stable and Scalable Method for Solving Initial Value PDEs with Neural Networks Marc Finzi Andres Potapczynski M. Choptuik A. Wilson 13 12 0 28 Apr 2023
A Survey on Solving and Discovering Differential Equations Using Deep Neural Networks Hyeonjung Jung Jung Jayant Gupta B. Jayaprakash Matthew J. Eagon Harish Selvam Carl Molnar W. Northrop Shashi Shekhar AI4CE 35 5 0 26 Apr 2023
New Designed Loss Functions to Solve Ordinary Differential Equations with Artificial Neural Network Xiao Xiong 16 0 0 29 Dec 2022
Physics-informed Neural Networks with Periodic Activation Functions for Solute Transport in Heterogeneous Porous Media Salah A. Faroughi Ramin Soltanmohammad Pingki Datta S. K. Mahjour S. Faroughi 13 22 0 17 Dec 2022
Multilayer Perceptron-based Surrogate Models for Finite Element Analysis Lawson Oliveira Lima Julien Rosenberger E. Antier Frédéric Magoulès AI4CE 9 0 0 17 Nov 2022
A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs Songming Liu Zhongkai Hao Chengyang Ying Hang Su Jun Zhu Ze Cheng AI4CE 16 17 0 06 Oct 2022
Semi-analytic PINN methods for singularly perturbed boundary value problems G. Gie Youngjoon Hong Chang-Yeol Jung PINN 8 5 0 19 Aug 2022
Learning Relaxation for Multigrid Dmitry Kuznichov AI4CE 18 1 0 25 Jul 2022
Anisotropic, Sparse and Interpretable Physics-Informed Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran AI4CE 19 0 0 01 Jul 2022
Physics Informed Neural Fields for Smoke Reconstruction with Sparse Data Mengyu Chu Lingjie Liu Q. Zheng Erik Franz Hans-Peter Seidel Christian Theobalt Rhaleb Zayer AI4CE 28 53 0 14 Jun 2022
BI-GreenNet: Learning Green's functions by boundary integral network Guochang Lin Fu-jun Chen Pipi Hu Xiang Chen Junqing Chen Jun Wang Zuoqiang Shi 34 20 0 28 Apr 2022
Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next S. Cuomo Vincenzo Schiano Di Cola F. Giampaolo G. Rozza Maizar Raissi F. Piccialli PINN 26 1,179 0 14 Jan 2022
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
Blaschke Product Neural Networks (BPNN): A Physics-Infused Neural Network for Phase Retrieval of Meromorphic Functions Juncheng Dong Simiao Ren Yang Deng Omar Khatib Jordan M. Malof Mohammadreza Soltani Willie J. Padilla Vahid Tarokh 25 0 0 26 Nov 2021
Physics informed neural networks for continuum micromechanics Alexander Henkes Henning Wessels R. Mahnken PINN AI4CE 13 139 0 14 Oct 2021
A Review of Physics-based Machine Learning in Civil Engineering S. Vadyala S. N. Betgeri J. Matthews Elizabeth Matthews AI4CE 25 152 0 09 Oct 2021
Solving the Dirichlet problem for the Monge-Ampère equation using neural networks K. Nystrom Matias Vestberg 26 2 0 07 Oct 2021
Learning in Sinusoidal Spaces with Physics-Informed Neural Networks Jian Cheng Wong C. Ooi Abhishek Gupta Yew-Soon Ong AI4CE PINN SSL 18 76 0 20 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
Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations Benjamin Moseley Andrew Markham T. Nissen‐Meyer PINN 45 209 0 16 Jul 2021
Cell-average based neural network method for hyperbolic and parabolic partial differential equations Changxin Qiu Jue Yan 14 10 0 02 Jul 2021
Legendre Deep Neural Network (LDNN) and its application for approximation of nonlinear Volterra Fredholm Hammerstein integral equations Z. Hajimohammadi Kourosh Parand A. Ghodsi 28 4 0 27 Jun 2021
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs Jérome Darbon P. Dower Tingwei Meng 8 22 0 07 May 2021
Efficient training of physics-informed neural networks via importance sampling M. A. Nabian R. J. Gladstone Hadi Meidani DiffM PINN 71 222 0 26 Apr 2021
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks N. Sukumar Ankit Srivastava PINN AI4CE 41 241 0 17 Apr 2021
Evolutional Deep Neural Network Yifan Du T. Zaki 16 68 0 18 Mar 2021
SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran PINN AI4CE 27 76 0 25 Feb 2021
A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate Hongwei Guo X. Zhuang Timon Rabczuk AI4CE 19 433 0 04 Feb 2021
Bayesian neural networks for weak solution of PDEs with uncertainty quantification Xiaoxuan Zhang K. Garikipati AI4CE 46 11 0 13 Jan 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 30 21 0 13 Jan 2021
Can Transfer Neuroevolution Tractably Solve Your Differential Equations? Jian Cheng Wong Abhishek Gupta Yew-Soon Ong 26 21 0 06 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
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning Fan Chen J. Huang Chunmei Wang Haizhao Yang 15 30 0 15 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 34 29 0 11 Dec 2020
Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture S. Niaki E. Haghighat Trevor Campbell Xinglong Li R. Vaziri AI4CE 13 203 0 27 Nov 2020
Symbolically Solving Partial Differential Equations using Deep Learning Maysum Panju Kourosh Parand A. Ghodsi 6 3 0 12 Nov 2020
A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder Youngkyu Kim Youngsoo Choi David Widemann T. Zohdi AI4CE 9 188 0 25 Sep 2020
Discovery of Governing Equations with Recursive Deep Neural Networks Jia Zhao Jarrod Mau PINN 17 6 0 24 Sep 2020
Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory Tao Luo Haizhao Yang 24 73 0 28 Jun 2020
Space-time deep neural network approximations for high-dimensional partial differential equations F. Hornung Arnulf Jentzen Diyora Salimova AI4CE 14 19 0 03 Jun 2020
DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization Rishikesh Ranade C. Hill Jay Pathak AI4CE 48 123 0 17 May 2020
SciANN: A Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks E. Haghighat R. Juanes AI4CE PINN 4 21 0 11 May 2020
On Calibration Neural Networks for extracting implied information from American options Shuaiqiang Liu Álvaro Leitao Anastasia Borovykh C. Oosterlee 8 3 0 31 Jan 2020