NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs

4 October 2021

Aditya Balu

Baskar Ganapathysubramanian

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Papers citing "NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs"

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Title
U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow Gege Wen Zong-Yi Li Kamyar Azizzadenesheli Anima Anandkumar S. Benson AI4CE 57 374 0 03 Sep 2021
Characterizing possible failure modes in physics-informed neural networks Aditi S. Krishnapriyan A. Gholami Shandian Zhe Robert M. Kirby Michael W. Mahoney PINN AI4CE 91 626 0 02 Sep 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sizhuang He P. Perdikaris AI4CE 47 122 0 09 Jun 2021
Distributed Multigrid Neural Solvers on Megavoxel Domains Aditya Balu Sergio Botelho Biswajit Khara Vinay Rao Chinmay Hegde Soumik Sarkar Santi S. Adavani A. Krishnamurthy Baskar Ganapathysubramanian AI4CE 83 11 0 29 Apr 2021
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks N. Sukumar Ankit Srivastava PINN AI4CE 111 246 0 17 Apr 2021
SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran PINN AI4CE 71 77 0 25 Feb 2021
Hybrid FEM-NN models: Combining artificial neural networks with the finite element method Sebastian K. Mitusch S. Funke M. Kuchta AI4CE 94 97 0 04 Jan 2021
Deep Generative Models that Solve PDEs: Distributed Computing for Training Large Data-Free Models Sergio Botelho Ameya Joshi Biswajit Khara Soumik Sarkar Chinmay Hegde Santi S. Adavani Baskar Ganapathysubramanian AI4CE 26 6 0 24 Jul 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs Siddhartha Mishra Roberto Molinaro PINN 40 263 0 29 Jun 2020
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs Siddhartha Mishra Roberto Molinaro PINN 45 172 0 29 Jun 2020
Implicit Neural Representations with Periodic Activation Functions Vincent Sitzmann Julien N. P. Martel Alexander W. Bergman David B. Lindell Gordon Wetzstein AI4TS 107 2,516 0 17 Jun 2020
Network size and weights size for memorization with two-layers neural networks Sébastien Bubeck Ronen Eldan Y. Lee Dan Mikulincer 51 33 0 04 Jun 2020
Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences Siddhartha Mishra T. Konstantin Rusch 68 49 0 26 May 2020
DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization Rishikesh Ranade C. Hill Jay Pathak AI4CE 123 125 0 17 May 2020
FEA-Net: A Physics-guided Data-driven Model for Efficient Mechanical Response Prediction Houpu Yao Yi Gao Yongming Liu AI4CE 87 66 0 31 Jan 2020
Understanding and mitigating gradient pathologies in physics-informed neural networks Sizhuang He Yujun Teng P. Perdikaris AI4CE PINN 87 292 0 13 Jan 2020
PyTorch: An Imperative Style, High-Performance Deep Learning Library Adam Paszke Sam Gross Francisco Massa Adam Lerer James Bradbury ... Sasank Chilamkurthy Benoit Steiner Lu Fang Junjie Bai Soumith Chintala ODL 319 42,038 0 03 Dec 2019
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations E. Kharazmi Z. Zhang George Karniadakis 58 241 0 27 Nov 2019
An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications E. Samaniego C. Anitescu S. Goswami Vien Minh Nguyen-Thanh Hongwei Guo Khader M. Hamdia Timon Rabczuk X. Zhuang PINN AI4CE 180 1,359 0 27 Aug 2019
Solving Irregular and Data-enriched Differential Equations using Deep Neural Networks C. Michoski M. Milosavljević Todd A. Oliver D. Hatch AI4CE 25 22 0 10 May 2019
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data Yinhao Zhu N. Zabaras P. Koutsourelakis P. Perdikaris PINN AI4CE 75 860 0 18 Jan 2019
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations Siyu Dai Shawn Schaffert Andreas G. Hofmann 107 359 0 05 Nov 2018
CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks Michela Paganini Luke de Oliveira Benjamin Nachman AI4CE GAN 43 314 0 21 Dec 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 113 1,373 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 77 2,048 0 24 Aug 2017
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations M. Raissi George Karniadakis AI4CE PINN 65 1,134 0 02 Aug 2017
Accelerating Eulerian Fluid Simulation With Convolutional Networks Jonathan Tompson Kristofer Schlachter Pablo Sprechmann Ken Perlin 80 530 0 13 Jul 2016
3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation Özgün Çiçek Ahmed Abdulkadir S. Lienkamp Thomas Brox Olaf Ronneberger 3DV 3DPC SSeg 3DH 135 6,483 0 21 Jun 2016
U-Net: Convolutional Networks for Biomedical Image Segmentation Olaf Ronneberger Philipp Fischer Thomas Brox SSeg 3DV 1.4K 76,547 0 18 May 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 1.2K 149,474 0 22 Dec 2014