Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion

30 September 2021

Papers citing "Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusion"

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Title
Solving 2-D Helmholtz equation in the rectangular, circular, and elliptical domains using neural networks D. Veerababu Prasanta K. Ghosh 81 0 0 26 Mar 2025
Estimation of the Acoustic Field in a Uniform Duct with Mean Flow using Neural Networks D. Veerababu Prasanta K. Ghosh AI4CE 54 0 0 25 Mar 2025
SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran PINN AI4CE 66 77 0 25 Feb 2021
Physics-informed neural networks with hard constraints for inverse design Lu Lu R. Pestourie Wenjie Yao Zhicheng Wang F. Verdugo Steven G. Johnson PINN 64 503 0 09 Feb 2021
Training neural networks under physical constraints using a stochastic augmented Lagrangian approach A. Dener M. Miller R. Churchill T. Munson Choong-Seock Chang 13 22 0 15 Sep 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 49 452 0 07 Sep 2020
Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers Yuying Liu N. Kutz Steven L. Brunton AI4TS 32 76 0 22 Aug 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 118 42,038 0 03 Dec 2019
Machine Learning for Fluid Mechanics Steven Brunton B. R. Noack Petros Koumoutsakos AI4CE PINN 72 2,105 0 27 May 2019
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks Georgios Kissas Yibo Yang E. Hwuang W. Witschey John A. Detre P. Perdikaris AI4CE 96 368 0 13 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 63 860 0 18 Jan 2019
Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black-Scholes Partial Differential Equations Julius Berner Philipp Grohs Arnulf Jentzen 45 182 0 09 Sep 2018
A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations Philipp Grohs F. Hornung Arnulf Jentzen Philippe von Wurstemberger 34 169 0 07 Sep 2018
Deep Learning of Vortex Induced Vibrations M. Raissi Zhicheng Wang M. Triantafyllou George Karniadakis AI4CE 31 373 0 26 Aug 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 85 748 0 20 Jan 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 83 1,373 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 45 2,042 0 24 Aug 2017
TensorFlow: A system for large-scale machine learning Martín Abadi P. Barham Jianmin Chen Zhiwen Chen Andy Davis ... Vijay Vasudevan Pete Warden Martin Wicke Yuan Yu Xiaoqiang Zhang GNN AI4CE 278 18,300 0 27 May 2016
Identity Mappings in Deep Residual Networks Kaiming He Xinming Zhang Shaoqing Ren Jian Sun 255 10,149 0 16 Mar 2016
Deep Residual Learning for Image Recognition Kaiming He Xinming Zhang Shaoqing Ren Jian Sun MedIm 1.1K 192,638 0 10 Dec 2015
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 519 149,474 0 22 Dec 2014
Sequence to Sequence Learning with Neural Networks Ilya Sutskever Oriol Vinyals Quoc V. Le AIMat 244 20,467 0 10 Sep 2014
Neural Machine Translation by Jointly Learning to Align and Translate Dzmitry Bahdanau Kyunghyun Cho Yoshua Bengio AIMat 323 27,205 0 01 Sep 2014
Deep Learning in Neural Networks: An Overview Jürgen Schmidhuber HAI 136 16,311 0 30 Apr 2014
ADADELTA: An Adaptive Learning Rate Method Matthew D. Zeiler ODL 84 6,619 0 22 Dec 2012