Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

14 January 2022

S. Cuomo

Vincenzo Schiano Di Cola

Papers citing "Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next"

50 / 105 papers shown

Title
Large-scale Neural Solvers for Partial Differential Equations Patrick Stiller Friedrich Bethke M. Böhme R. Pausch Sunna Torge A. Debus J. Vorberger Michael Bussmann Nico Hoffmann AI4CE 31 26 0 08 Sep 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 68 452 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 109 896 0 28 Jul 2020
Machine learning for metal additive manufacturing: Predicting temperature and melt pool fluid dynamics using physics-informed neural networks Qiming Zhu Zeliang Liu Jinhui Yan PINN AI4CE 17 300 0 28 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 30 263 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 105 2,516 0 17 Jun 2020
Deep learning of free boundary and Stefan problems Sizhuang He P. Perdikaris 102 81 0 04 Jun 2020
A nonlocal physics-informed deep learning framework using the peridynamic differential operator E. Haghighat A. Bekar E. Madenci R. Juanes PINN 18 106 0 31 May 2020
Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations Christopher J. Arthurs A. King PINN 116 51 0 02 May 2020
A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture Dehao Liu Yan Wang 95 73 0 01 May 2020
EikoNet: Solving the Eikonal equation with Deep Neural Networks Jonathan D. Smith Kamyar Azizzadenesheli Zachary E. Ross 27 131 0 25 Mar 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 210 768 0 13 Mar 2020
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition E. Kharazmi Zhongqiang Zhang George Karniadakis 158 520 0 11 Mar 2020
Universal Differential Equations for Scientific Machine Learning Christopher Rackauckas Yingbo Ma Julius Martensen Collin Warner K. Zubov R. Supekar Dominic J. Skinner Ali Ramadhan Alan Edelman AI4CE 58 578 0 13 Jan 2020
Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport Qizhi He D. Barajas-Solano G. Tartakovsky A. Tartakovsky AI4CE 42 258 0 06 Dec 2019
Neural Tangents: Fast and Easy Infinite Neural Networks in Python Roman Novak Lechao Xiao Jiri Hron Jaehoon Lee Alexander A. Alemi Jascha Narain Sohl-Dickstein S. Schoenholz 54 227 0 05 Dec 2019
Variational Physics-Informed Neural Networks For Solving Partial Differential Equations E. Kharazmi Z. Zhang George Karniadakis 48 241 0 27 Nov 2019
Physics-Informed Neural Networks for Power Systems George S. Misyris Andreas Venzke Spyros Chatzivasileiadis PINN AI4CE 45 216 0 09 Nov 2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators Lu Lu Pengzhan Jin George Karniadakis 163 2,082 0 08 Oct 2019
PyDEns: a Python Framework for Solving Differential Equations with Neural Networks A. Koryagin R. Khudorozhkov S. Tsimfer OOD AI4CE 23 32 0 25 Sep 2019
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs Xuhui Meng Zhen Li Dongkun Zhang George Karniadakis PINN AI4CE 39 446 0 23 Sep 2019
DeepXDE: A deep learning library for solving differential equations Lu Lu Xuhui Meng Zhiping Mao George Karniadakis PINN AI4CE 82 1,513 0 10 Jul 2019
Physics Informed Extreme Learning Machine (PIELM) -- A rapid method for the numerical solution of partial differential equations Vikas Dwivedi Balaji Srinivasan PINN 46 191 0 08 Jul 2019
$Transfer learning enhanced physics informed neural network for phase-field modeling of fracture$ Transfer learning enhanced physics informed neural network for phase-field modeling of fracture S. Goswami C. Anitescu S. Chakraborty Timon Rabczuk PINN 39 602 0 04 Jul 2019
A Survey of Optimization Methods from a Machine Learning Perspective Shiliang Sun Zehui Cao Han Zhu Jing Zhao 39 554 0 17 Jun 2019
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks N. Geneva N. Zabaras AI4CE 27 270 0 13 Jun 2019
A Review of Deep Learning with Special Emphasis on Architectures, Applications and Recent Trends Saptarshi Sengupta Sanchita Basak P. Saikia Sayak Paul Vasilios Tsalavoutis Frederick Ditliac Atiah V. Ravi R. Peters AI4CE 73 332 0 30 May 2019
N-BEATS: Neural basis expansion analysis for interpretable time series forecasting Boris N. Oreshkin Dmitri Carpov Nicolas Chapados Yoshua Bengio AI4TS 90 1,026 0 24 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 103 368 0 13 May 2019
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks Dongkun Zhang Ling Guo George Karniadakis AI4CE 50 212 0 03 May 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Yaoyu Zhang Yan Xiao Zheng Ma 117 509 0 19 Jan 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 70 860 0 18 Jan 2019
Deep Neural Network Approximation Theory Dennis Elbrächter Dmytro Perekrestenko Philipp Grohs Helmut Bölcskei 37 210 0 08 Jan 2019
Reconciling modern machine learning practice and the bias-variance trade-off M. Belkin Daniel J. Hsu Siyuan Ma Soumik Mandal 174 1,628 0 28 Dec 2018
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yibo Yang P. Perdikaris AI4CE PINN 89 356 0 09 Nov 2018
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations Siyu Dai Shawn Schaffert Andreas G. Hofmann 99 359 0 05 Nov 2018
GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration Jacob R. Gardner Geoff Pleiss D. Bindel Kilian Q. Weinberger A. Wilson GP 68 1,088 0 28 Sep 2018
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 98 405 0 21 Sep 2018
Kernel Flows: from learning kernels from data into the abyss H. Owhadi G. Yoo 41 90 0 13 Aug 2018
Horovod: fast and easy distributed deep learning in TensorFlow Alexander Sergeev Mike Del Balso 59 1,218 0 15 Feb 2018
On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups Risi Kondor Shubhendu Trivedi MLT 100 497 0 11 Feb 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 99 751 0 20 Jan 2018
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 54 611 0 28 Nov 2017
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 68 912 0 28 Nov 2017
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 50 583 0 17 Nov 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 100 1,373 0 30 Sep 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 69 2,048 0 24 Aug 2017
A Brief Survey of Deep Reinforcement Learning Kai Arulkumaran M. Deisenroth Miles Brundage Anil Anthony Bharath OffRL 99 2,792 0 19 Aug 2017
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations M. Raissi George Karniadakis AI4CE PINN 58 1,134 0 02 Aug 2017
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis 53 267 0 29 Mar 2017